1/(1*3)+1/(2*4)+1/(3*5)+.+1/[n*(n+2)]=
问题描述：
1/(1*3)+1/(2*4)+1/(3*5)+.+1/[n*(n+2)]=
答
1/(1×3)=1/2(1/1-1/3)1/(2×4)=1/2(1/2-1/4)1/(3×5)=1/2(1/3-1/5)……1/[n(n+1)]=1/2[1/n-1/(n+1)]以上各式相加得：原式=1/2［1+1/2-1/(n+1)-1/(n+2)］=1/2*[3(n+1)(n+2)-2(n+2)-2(n+1)]/[2(n+1)(n+2)]=(3n^2+5n)/...