1/6*7+1/7*8+1/8*9+……+1/100*101=

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1/6*7+1/7*8+1/8*9+……+1/100*101=
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1/6*7+1/7*8+1/8*9+……+1/100*101=
1/6*7+1/7*8+1/8*9+……+1/100*101=

1/6*7+1/7*8+1/8*9+……+1/100*101=
1/(n*(n+1)) = 1/n - 1/(n+1)
因此
1/6*7 = 1/6 - 1/7
1/7*8 = 1/7 - 1/8
...
1/100*101 = 1/100 - 1/101
叠加后消去正负项
原式 = 1/6 - 1/101 = 95/606

1/n(n+1)=1/n-1/(n+1)
原式=1/6-1/7^1/7-1/8+……+1/100-1/101=1/6-1/101=95/606

=1/6-1/7+1/7-1/8+……+1/100-1/101= 1/6 - 1/101 = 95/606