已知数列an满足a1=1/2,an+1=an+1/n²+n,求an
问题描述：
已知数列an满足a1=1/2,an+1=an+1/n²+n,求an
答
a(n+1)=an +1/(n²+n)=an +1/[n(n+1)]=an +1/n -1/(n+1)
a(n+1) +1/(n+1)=an +1/n
a1+1/1=1/2 +1=3/2,数列{an +1/n}是各项均为3/2的常数数列.
an +1/n=3/2
an=3/2 -1/n