数列求和1/1*3,1/2*4,1/3*5...1/n(n+2)

问题描述:

数列求和1/1*3,1/2*4,1/3*5...1/n(n+2)
RT

1/1*3=(1/2)(1-1/3)1/2*4=(1/2)(1/2-1/4)...1/n(n+2)=(1/n - 1/(n+2))/2 原式=(1/2)(1-1/3+1/2-1/4+...+1/(n-1)-1/(n+1)+1/(n)-1/(n+2))=(1/2)(1+1/2-1/(n+1)-1/(n+2))=3/4-(2n+3)/2(n+1)(n+2)