1/1*2*3+1/2*3*4+1/3*4*5+...+1/98*99*100等于多少?
问题描述：
1/1*2*3+1/2*3*4+1/3*4*5+...+1/98*99*100等于多少?
答
an=1/2n+1/2(n+2)-1/(n+1)
1/1*2*3+1/2*3*4+1/3*4*5+...+1/98*99*100
=(1/2+1/6-1/2)+(1/4+1/8-1/3)+...+(1/196+1/200-1/99)
=0.5*(1+1/2+...+1/98)+0.5*(1/3+1/4+...+1/100)-(1/2+1/3+1/4+...+1/99)
=0.5*(1+1/2+1/99+1/100)-1/2-1/99
=4949/19800