设f(n)=1比(n+1)+1比(n+2)+1比(n+3)+……+1比2n （n=1,2,3...)则f(n+1)-f(n)+?
问题描述：
设f(n)=1比(n+1)+1比(n+2)+1比(n+3)+……+1比2n （n=1,2,3...)则f(n+1)-f(n)+?
是f（n+1）-f（n)=?
答
f(n)有n项,则
f(n+1)-f(n)
=[(1/(n+2))+(1/(n+3))+···+(1/(2n))+(1/(2n+1))+(1/(2n+2))]
-[(1/(n+1))+(1/(n+2))+···+(1/(2n))]
=[(1/(2n+1))+(1/(2n+2))]-(1/(n+1))
=(1/(2n+1))-(1/(2n+2))
=1/(2(n+1)(2n+1))