a1=1,a(n+1)=(1/2)*an+1/(2^n)求an

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a1=1,a(n+1)=(1/2)*an+1/(2^n)求an

a1=1,a(n+1)=(1/2)*an+1/(2^n)求an
a1=1,a(n+1)=(1/2)*an+1/(2^n)
求an

a1=1,a(n+1)=(1/2)*an+1/(2^n)求an
2^(n+1)a(n+1)=2^(n)an+2 (n∈N*)
=>{2^(n)an}为等差数列
=>2^(n)an=2^(n-1)+a1*2
=>an=n/(2^(n-1)) (n>1)
=>a1=1=1/(2^(1-1))
=>an=n/(2^(n-1)) (n∈N*)
一楼的写错了.

题目没错吧? 确定是1/2*an?

之前写错了,实在是不好意思啊!已经更正过来了!

两边同乘以2^(n+1)
2^(n+1)a(n+1)=2^(n)an+2 (n∈N*)
∴{2^(n)an}为等差数列
∴2^(n)an=2*(n-1)+a1*2=2n-2+2=2n
∴an=n/[2^(n-1))] (n>1)
又a1=1=1/[2^(1-1)]
∴an=n/[2^(n-1)] (n∈N*)