Question

已知数列an中,an+1+(-1)^an=2n-1,则数列an前12项和S12= 78

Answer 1

a'n+1' + [(-1)^n] an = 2n-1 (1)

a'n+2' + [(-1)^(n+1)] a'n+1' = 2(n+1) -1 =2n+1 (2)

式(1) * (-1)^n + 式(2), 注意到 (-1)^(n+1) = - (-1)^n , 有

an + a‘n+2’=[(-1)^n] (2n-1) + (2n+1)

n值和上式左边的关系如下：

1 a1+a3

2 a2+a4

5 a5+a7

6 a6+a8

9 a9+a11

10 a10+a12

现在看清楚了吧,呵呵