求证:1/(2*3)+1/(3*5)+...+1/[(n+1)(2n+1)]
问题描述：
求证:1/(2*3)+1/(3*5)+...+1/[(n+1)(2n+1)]
答
这个方法叫裂项
如1/2*3 =1/2 - 1/3
1/3*5 =1/2(1/3 - 1/5)
1/[(n+1)(2n+1)]=1/n[1/(n+1) - 1/(2n+1)]
=1/n(n+1)-1/n(2n+1)