1/2+1/6+1/12+.+[1/(n-1)n] +[1/(n+1)n]等于多少

问题描述:

1/2+1/6+1/12+.+[1/(n-1)n] +[1/(n+1)n]等于多少

1/2+1/6+1/12+.+[1/(n-1)n] +[1/(n+1)n]
=1-1/2+1/2-1/3+1/3-1/4.+1/n-1/(n+1)=1-1/(n+1)希望有解题分析1/2=1-1/21/6=1/2-1/3.....[1/(n-1)n] =1/(n-1)-1/n[1/(n+1)n]=1/n-1/(n+1)代入原式即可.