如果f(n)=1/(n+1)+1/(n+2)+```1/2n (n属于N*）那么f(n+1)-f(n)=_数学解答

如果f(n)=1/(n+1)+1/(n+2)+```1/2n (n属于N*）那么f(n+1)-f(n)=

人气：183 ℃　时间：2020-09-13 13:42:38

解答

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))
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