Question

数列an+1=2an+2 的n次方。求an

Answer 1

a(n+1)=2an+2^n (2^n表示2的n次）两边同除以2^(n+1)
a(n+1)/2^(n+1)=an/2^n+1/2
a(n+1)/2^(n+1)-an/2^n=1/2
所以{an/2^n}是以a1/2为首相d=1/2为公差的等差数列
an/2^n=a1/2+(n-1)/2
an=2^na1/2+(n-1)2^n/2
你题目缺少条件a1

Answer 2

a(n+1)=2an+2^n
a(n+1)+2^n=2an+2*2^n
a(n+1)+2^n=2(an+2^n)
[a(n+1)+2^n]/(an+2^n)=2
所以an+2^n是以a1+2，公比为2的等比数列

因为差条件，所以无法求出an

Answer 3

-1