{n(n+1)(n+2)}分之一怎样求和

题目

{n(n+1)(n+2)}分之一怎样求和

答案

1/(n(n+1)(n+2)=(1/2)*2/n(n+1)(n+2)=(1/2)*[(n+2)-n]/n(n+1)(n+2)=(1/2)*[(n+2)/n(n+1)(n+2)-n/n(n+1)(n+2)]=(1/2)*[1/n(n+1)-1/(n+1)(n+2)]所以1/1*2*3+……+1/n(n+1)(n+2)=(1/2)*[1/1*2-1/2*3+……+1/n(n+1)-1/(n...