设
,
.如果存在
使得
,那么就说
可被
整除(或
整除
),记做
且称
是
的倍数,
是
的约数(也可称为除数、因数).
不能被
整除就记做
.由整除的定义,不难得出整除的下面几条性质:①若
,
,则
;②
,
互质,若
,
,则
;③若
,则
,其中
.
(1)若数列
满足,
,其前
项和为
,证明:
;
(2)若
为奇数,求证:
能被
整除;
(3)对于整数
与
,
,求证:
可整除
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b72ea8ec0d9f8b1cfc4de834b8bfb608.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87803b7cee18366b89d51799250df510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6705dba65746e1d4cac6a268b3c806ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/020e12ff4f028aba3a205a95e650d72b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79bda3d07c2fef4d6af4a13ade4c743e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/020e12ff4f028aba3a205a95e650d72b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e4d6df2a57b7e5be32c05c10257ea6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91638bacbf4d15736d26713ba90e0fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91638bacbf4d15736d26713ba90e0fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e4d6df2a57b7e5be32c05c10257ea6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0601879ae4ca9592246d135bfa48658c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383eb235f8e0ceda13367b16d29e0180.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/503618b9bfb53a06f0ec6a5e427dcdbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0da20edf2714109dcfded7e212ec44a.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e12059d1dac926a235ccd40c3b61b1b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed9dbd8ed61db4f1c14f6b0e5f071200.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1e4de97f8490fddcff16afe8583266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
(3)对于整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b96cdd9e003120b6102d927dbf53e39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5009ce2d56180d31204f77c871fb375c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b326965628b5d967aafe9e696fdc07.png)
更新时间:2024-06-09 22:56:39
|
相似题推荐
解答题-证明题
|
困难
(0.15)
名校
解题方法
【推荐1】已知
(
)
(1)若
对
恒成立,求实数a范围;
(2)求证:对
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6ae3a06e2db61ce958f143eb7f7390b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
(2)求证:对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5141a5b907f5ff11bbd7cacbd7b5db3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e4d16e77a13cb72c849cac26c8ae54e.png)
您最近一年使用:0次
【推荐2】已知数列
的首项
,
,
.
(1)求
的通项公式;
(2)证明:对任意的
,
,
;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc6545b8eca1c4223ed701a199a85683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7643e8b7aa32ebf299048417a94432dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac2c67be0e344a21e582980c0431c24.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)证明:对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cd868bb05899fb3942c32cdb7d547b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac2c67be0e344a21e582980c0431c24.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78eca1f732051ae5f4fdfdb139c14672.png)
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【推荐1】对于整数除以某个正整数的问题,如果只关心余数的情况,就会产生同余的概念.关于同余的概念如下:用给定的正整数
分别除整数
,若所得的余数(小于正整数
的自然数,即0,1,
)相等,则称
对模
同余,记作
.例如:因为
,
,所以
;因为
,所以
.表示对模
同余关系的式子叫做模
的同余式,简称同余式,同余式的记号
是高斯在1800年首创.两个同模的同余式也能够进行加法和减法运算,其运算规则如下:已知整数
,正整数
,若
,则
,
.阅读上述材料,解决下列问题:
(1)若
,且整数
,求
的值;
(2)已知整数
,正整数
,证明:若
,则
;
(3)若
,其中
为正整数,
为非负整数,证明:
能被11整除的充要条件为
能被11整除.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18c18c0cebecdfc0f63f64b98b8618f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bf17f75882ab0a28a78c8c49d1d1255.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135a1a6b030325a6b417d3d5fecb8778.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0bd5638bfe2f006ab5f707f5039a160.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d62bbd00daf6bbdde9b3d936ab4f2ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a65d0f1fb1b4f913af5741ebe2e98d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18eae33f07a441a87b75445811e87c27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bf17f75882ab0a28a78c8c49d1d1255.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d10449bc77d692a7270e0f20a68cdf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfa91f51e5e0650e3fae950da7cbf4a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3113592ea3c033253299a0bdbb619897.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d51c59ce2cd593666329587abed347bf.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f1774978271a3e5a0b970b47de774f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08fc88e26cec31df99dfa1824587ae30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)已知整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d10449bc77d692a7270e0f20a68cdf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfa91f51e5e0650e3fae950da7cbf4a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce06d8c49a3c57e5cf10e773818a2467.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f966aecd0328697920c0b7a22726cd33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b65a63629464f5a2c90356e367f66be.png)
您最近一年使用:0次
解答题-问答题
|
困难
(0.15)
解题方法
【推荐2】设数列
的前
项和为
,已知
,且
.
(1)证明:
为等比数列,并求数列
的通项公式;
(2)设
,若对于任意的
,不等式
恒成立,求实数
的取值范围;
(3)高斯是德国著名数学家,近代数学的奠基者之一,享有“数学王子”的称号,用他名字定义的函数称为高斯函数
,其中
表示不超过
的最大整数,如
,
,设
,数列
的前
项和为
,求
除以16的余数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c32899ae4ebf40c57124b2cabba77ef2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1928c254cfada1f75a5cd1e34db5a63.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b1b04112db77069cb75ad66501d564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3b8dd6deb75e13a84f153070d22f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf3fb678d1de9b83ae7ab8bfe0cc25e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)高斯是德国著名数学家,近代数学的奠基者之一,享有“数学王子”的称号,用他名字定义的函数称为高斯函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1550a97c21c1d71c9e95dde569668be0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d54a0e82778f606d95a486835ac9f56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f2323cbdf0b1b71092c962ae705102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dfc2d1084094bb015f11974a10c26b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb3200f3cc24af2c9663b5c0de282810.png)
您最近一年使用:0次
解答题-问答题
|
困难
(0.15)
名校
解题方法
【推荐1】已知
.
(1)若
,求
;
(2)若
,求
除以9的余数;
(3)若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede06576270baa407ccdf75d63fff70e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677e46ecd051c92489c0d1d458932f37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae8f5e8af9db93e247c639809c523f6b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98a56a5248f0eebbc362493c2b648312.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed612e4741d2b861ad957d36a2e32cda.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c129c4b3b557f91e456ad41b7e3fe0ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae48677f8f6e1eaa980756a18378e593.png)
您最近一年使用:0次
解答题-问答题
|
困难
(0.15)
名校
【推荐2】已知
为正整数,对于给定的函数
,定义一个
次多项式
如下:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18970eb9afce70d15d8b276535427df2.png)
(1)当
时,求
;
(2)当
时,求
;
(3)当
时,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c64d8ccd22b77a2b30da084d30d2e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18970eb9afce70d15d8b276535427df2.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28638f8c054a7bb4d9b46fde330bc76f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c64d8ccd22b77a2b30da084d30d2e04.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e44284cb19805a584880a686ac3df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c64d8ccd22b77a2b30da084d30d2e04.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1c079afd1b058adc67a50f48f3d466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c64d8ccd22b77a2b30da084d30d2e04.png)
您最近一年使用:0次
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名校
【推荐1】设集合
是由数列
组成的集合,其中数列
同时满足以下三个条件:
①数列
共有
项,
;②
;③![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1630b48586ff6a1469ab1dfb2901d195.png)
(1)若等比数列
,求等比数列
的首项、公比和项数;
(2)若等差数列
是递增数列,并且
,常数
,求该数列的通项公式;
(3)若数列
,常数
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7f2c72ab559a0615db4c51327b78d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
①数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96a5d7258973bf6c6afab73fcc1e8263.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/978585d683394ec4818e8c88ac6905eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1630b48586ff6a1469ab1dfb2901d195.png)
(1)若等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88881f3b91fd351c690cfed34dfede02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fee2ebbfb88befdb0ac25da2ddfc86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09659bc38dd8ea03bcd91fdfe7907ee.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba0dd42b8ff4e9893d5afd641da0600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a899d786e1c9ca96e401f07bea4e55b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ac49ab7c8001c209b8611b9ea40d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeeb4c45bca6db66be8f99c381b73284.png)
您最近一年使用:0次
解答题-证明题
|
困难
(0.15)
【推荐2】若数列
满足
,数列
为
数列,记
.
(1)写出一个满足
,且
的
数列
;
(2)若
,
,证明:E数列
是递增数列的充要条件是
;
(3)对任意给定的整数
,是否存在首项为
的
数列
,使得
?如果存在,写出一个满足条件的
数列
;如果不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/786d6bfda2130196e2050c0439de7897.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f269e4e96c27fc6538af64a5a54a023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf1ec142aee1bd8b3fe42687b346b462.png)
(1)写出一个满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/230af4df0d4a02ba90ed01feed036650.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d86d0bbe420c44e9526776a3fb2d5cda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8827c05075967f3c3569d31cb6b83919.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e58777a9c14f76127552af0906eeeaf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ca967d2f5ea038668c650881de0dfc.png)
(3)对任意给定的整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4f27f84764f1cca89ce3d93fc1cf603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89726ddaa0e0b461bebe2efc831b0c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
您最近一年使用:0次