1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+……1/(98*99*100)简便算法及答案
问题描述：
1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+……1/(98*99*100)简便算法及答案
答
首先写出这个式子的通项a(n)=1/(n*(n+1)*(n+2))所以a(n)+a(n+1)=1/(n*(n+1)*(n+2))+1/((n+1)*(n+2)*(n+3))=(2n+3)/(n*(n+1)*(n+2)*(n+3))=1/(n*(n+2))-1/((n+1)*(n+3))写成这个样子就很简单了a1+a2=1/1*3-1/2*4a2+a3...