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求解1/(2*7)+1/(7*12)+1/(12*17)+1/(17*22)+1/(22*27)简单算法
题目详情
求解1/(2*7)+1/(7*12)+1/(12*17)+1/(17*22)+1/(22*27)
简单算法
简单算法
▼优质解答
答案和解析
1/(2*7)+1/(7*12)+1/(12*17)+1/(17*22)+1/(22*27)
=(1/2-1/7)*1/5+(1/7-1/12)*1/5+(1/12-1/17)*1/5+(1/17-1/22)*1/5+(1/22-1/27)*1/5
=(1/2-1/7+1/7-1/12+1/12-1/17+1/17-1/22+1/22-1/27)*1/5
=(1/2-1/27)*1/5
=25/54*1/5
=5/54
=(1/2-1/7)*1/5+(1/7-1/12)*1/5+(1/12-1/17)*1/5+(1/17-1/22)*1/5+(1/22-1/27)*1/5
=(1/2-1/7+1/7-1/12+1/12-1/17+1/17-1/22+1/22-1/27)*1/5
=(1/2-1/27)*1/5
=25/54*1/5
=5/54
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