问题 选择题

数列{an}满足an+1+(-1)nan=2n-1,则{an}的前60项和为(  ).

A.3 690

B.3 660

C.1 845

D.1 830

答案

答案:D

an+1+(-1)nan=2n-1,

n=2k时,a2k+1a2k=4k-1,

n=2k-1时,a2ka2k-1=4k-3,

从而a2k+1a2k-1=2,a2k+3a2k+1=2,

因此a2k+3a2k-1

a1a5a9=…=a61

于是S60a1a2a3+…+a60

=(a2a3)+(a4a5)+…+(a60a61)

=3+7+11+…+(2×60-1)==1 830.

单项选择题
单项选择题