1/20+1/30+1/42······+1/132 简算 帮帮忙!

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1/20+1/30+1/42······+1/132简算帮帮忙!1/20+1/30+1/42······+1/132简算帮帮忙!1/20+1/30+1/42······+1/132简算帮帮忙!20=4

1/20+1/30+1/42······+1/132 简算 帮帮忙!
1/20+1/30+1/42······+1/132 简算 帮帮忙!

1/20+1/30+1/42······+1/132 简算 帮帮忙!
20=4*5
30=5*6
...
132=11*12
1/20 = 1/（4*5）=1/4 - 1/5
1/30 =1/5 - 1/6
...
1/132 =1/11 - 1/12
左边相加是原式= 右边相加=1/4 - 1/12 =1/6

答案:1/6
解析：本题是裂项相加 原式=1/4*5+1/5*6+........+1/11*12
=(1/4-1/12)*1/1=2/12=1/6

显然20=4*5 30=5*6 42=6*7....132=11*12
所以采用裂项求和
1/20+1/30+1/42+.....+1/132=1/(4*5)+1/(5*6)+....+1/(11*12)
=1/4-1/5+1/5-1/6+.....+1/11-1/12
=1/4-1/12
=1/6

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