计算:1/(1*2*3)+1/(2*3*4)+.+1/[n(n+1)(n+2)]
问题描述：
计算:1/(1*2*3)+1/(2*3*4)+.+1/[n(n+1)(n+2)]
1/(1*2*3)+1/(2*3*4)+.+1/[n(n+1)(n+2)]
是 要 用 什 么 方 法
答
1/[n(n+1)(n+2)]
=1/2*[1/n(n+1)-1/(n+1)(n+2)]
所以原式=1/2*[1/1*2-1/2*3+……+1/n(n+1)-1/(n+1)(n2)]
=1/2*[1/1*2-1/(n+1)(n+2)]
=(n²+3n)/(4n²+12n+8)