利用发现计算1/2+1/6+1/12+1/20+1/30+1-查字典问答网

来自任红菊的问题

　　利用发现计算1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90的详细答案

1回答

2020-05-14 17:00

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马瑞晓

　　1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90

　　=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)+1/(8*9)+1/(9*10)

　　=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10

　　=1-1/10

　　=9/10

2020-05-14 17:04:17

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