设f(n)=1/(n+1)+1/(n+2)+1/(n+3)+…+1/2n(n∈N),那么f(n+1)-f(n)等于___
这个题目偶算了N次结果均为:1/(2n+1)+1/(n+1),与答案就是不同,也不知道是怎么回事?希望写明详细过程,感谢大家了啊!!
參考答案:f(n+1)=1/(n+2)+1/(n+3)+1/(n+4)+...+1/2n+1/(2n+1)+1/(2n+2)
f(n)=1/(n+1)+1/(n+2)+1/(n+3)+…+1/2n
f(n+1)-f(n)=1/(2n+1)+1/(2n+2)-1/(n+1)
=1/(2n+1)-1/(2n+2)