1 . 设等差数列
的首项为0,公差为a,
;等差数列
的首项为0,公差为b,
.由数列
和
构造数表M,与数表
;
记数表M中位于第i行第j列的元素为
,其中
,(i,j=1,2,3,…).
记数表
中位于第i行第j列的元素为
,其中
(
,
,
).如:
,
.
(1)设
,
,请计算
,
,
;
(2)设
,
,试求
,
的表达式(用i,j表示),并证明:对于整数t,若t不属于数表M,则t属于数表
;
(3)设
,
,对于整数t,t不属于数表M,求t的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67f0d538cab3daae7d590482989f2a35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/254fa569dc952c0b78fed34c8a1daf97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bac0147b641a350b592ae6a8b565a8d.png)
记数表M中位于第i行第j列的元素为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e69701dd0e5844cd75752cd391deef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49128aead2182911b2d154bf8bcd1cf2.png)
记数表
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bac0147b641a350b592ae6a8b565a8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cbc4957c304de68d181441625394edb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0227d02cc5bfa2845d30512262a47ae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b2d219599bb6453e9b8b431a948ecf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7965f5d265d8b1a5bea91a427dd3a21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3aabd97c086e3e1a7fcf4a419d0adf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef914cefc04d21daa7a7ec165f1d269b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c251824d22684ccb464a910c27f2e204.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab839d8569171afab5ed55c22013aa72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86718fa3bd81961f00798692fbf86db1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e05b891c5f036025713d20bf44c20704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c75905e8c61af58a59edd945b054da6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ecbb868da9359eec873a17e530b634f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f08ce80e91fdf435a8e3ec05be990e9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab1c19b66cda3fb899f06d9a25e973c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e69701dd0e5844cd75752cd391deef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cbc4957c304de68d181441625394edb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bac0147b641a350b592ae6a8b565a8d.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f08ce80e91fdf435a8e3ec05be990e9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab1c19b66cda3fb899f06d9a25e973c.png)
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