1/2+1/6+1/12+1/20+······+1/72+1/90

Question

求计算过程及思考办法！

Answer 1

解答：
就是裂项，将分数写成两个分数的和
1/n(n+1)=1/n-1/(n+1)

1/2+1/6+1/12+1/20+······+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)
=(1/1-1/2)+(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

Answer 2

你好！
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
＝1-1/2+1/2-1/3+1/3-1/4+……1/9-1/10 （除了1与1/10，两两抵消）
＝1-1/10
＝9/10
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