已知数列{an}满足a1=1/2,an+1=an+1/n的平方+n求an

问题描述:

已知数列{an}满足a1=1/2,an+1=an+1/n的平方+n求an

an+1=an+1/n的平方+nan+1-an=1/n^2+nan+1-an=1/n(n+1)an+1-an=(1/n)-1/(n+1)an-an-1=(1/n-1)-1/nan-1-an-2=(1/n-2)-1/(n-1).a2-a1=1/1-1/2an-a1=1-1/nan=1-1/n+1/2an=3/2-1/n