设计算法求1/(1*2)+1/(2*3)+1/(3*4)+……+1/(99*100)的值
题目
设计算法求1/(1*2)+1/(2*3)+1/(3*4)+……+1/(99*100)的值
答案
1/(1*2)+1/(2*3)+1/(3*4)+……+1/(99*100)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+.+(1/99-1/100)
=1-1/100
=99/100
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