求:a1=1,a(n+1)=an+1/n(n+1)的通项公式

Question

求解答答案

Answer 1

a(n+1)=an+1/n-1/(n+1)
a(n+1)+1/(n+1)=an+1/n
设bn=an+1/n
则：b(n+1)=bn
b1=a1+1/1=2
所以：数列bn为常数列bn=2
所以an+1/n=2
an=2-1/n本回答被提问者采纳

Answer 2

An=2-1/n
A(n+1)-An=1/n(n+1)=1/n-1/n+1
A2-A1=1-1/2
A3-A2=1/2-1/3
.............
An-An-1=1/(n-1)-1/n
累加
An-A1=1-1/n