已知函数f(x)=1/x×(x+1)则f(1)+……+f(n)=14/15

Question

已知函数f(x)=1/x×(x+1)则f(1)+……+f(n)=14/15

Answer 1

f(x)=1/x(x+1)=1/x-1/(x+1)
则f(1)+f(2)+...+f(n)
=1-1/2+1/2-1/3+...+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)
=14/15
所以n=14
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