Question

对于正整数x，线定义f(x)=2/x(x+2)，则有f(1)=2/1×3，f(2)=2/2×4……

试求：f(1)+f(2)+f(3)+……+f(n-1)+f(n)的值（其中n为正整数）

Answer 1

f(x)=(1/x)-(1/(x+2))
所以f(1)+.....f(n)=1-1/3+1/2-1/4+1/3-1/5+........(1/n)-(1/(n+2))=1+1/2-(1/(n+1))-(1/(n+2))
此题注意化分，找规律即可
希望可以帮到你

Answer 2

f(x)=2/[x(x+2)]
=(1/x)-[1/(x+2)]
f(1)+f(2)+f(3)+f(n-1)+f(n)
=1-(1/3)+(1/2)-(1/4)+(1/3)-(1/5)+……+[1/(n-1)]-[1/(n+1)]+(1/n)-[1/(n+2)]
=1+(1/2)-[1/(n+1)]-[1/(n+2)]