设计算法求1/(12)+1/(23)+1/(34)+……+1/(99100)的值

题目详情

设计算法求1/(1*2)+1/(2*3)+1/(3*4)+……+1/(99*100)的值

▼优质解答

答案和解析

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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