1/1X2+1/2x3+1/3x4+1/4x5+.+1/98x99+1/99x100求结果!
问题描述:
1/1X2+1/2x3+1/3x4+1/4x5+.+1/98x99+1/99x100求结果!
答
1/[n(n+1)]=1/n - 1/(n+1)
原式=1/1 - 1/2 + 1/2 - 1/3 +…+1/99 - 1/100
=1- 1/100
=0.99