已知数列{an}满足a1=1,an+1=an+2^n+n,则an=?

2024-12-13 01:52:59
推荐回答(2个)
回答1:

an+1=an+2^n+n
an=a(n-1)+2^(n-1)+n-1
...
a2=a1+2+1
a1=1
累加起来得
a(n+1)=2^n+2^(n-1)+...+1+n+(n-1)+...+1
a(n+1)=2^(n+1)-1+n(n+1)/2
所以an=2^n+n(n-1)/2-1

回答2:

思路:左右叠加n项和即可。(自己算)