1/1X2+1/2X3+1/3X4+...+1/n(n+1)等于几?
问题描述：
1/1X2+1/2X3+1/3X4+...+1/n(n+1)等于几?
答
原式=(2-1)/(1×2)+(3-2)/(2×3)+……+(n+1-n)/[n(n+1)]
=1-1/2+1/2-1/3+……+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)
温馨提示：分母部分要加上括号，否则答案是无穷大的
答
=1-1/2+1/2-1/3+1/3-1/4……+1/n-1/(n+1)=1-1/(n+1)=n/(n+1)