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(
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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)=?
是f(n+1)-f(n)=?
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))
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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