1/2+1/6+1/12+……+1/90=?计算过程和规律

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1/2+1/6+1/12+……+1/90=?计算过程和规律
1/2+1/6+1/12+……+1/90=?计算过程和规律

1/2+1/6+1/12+……+1/90=?计算过程和规律
1/2+1/6+1/12+……+1/90
=1/(1*2)+1/(2*3)+...+1/(8*9)+1/(9*10)
=1-1/2+1/2-1/3+...+1/8-1/9+1/9-1/10
=1-1/10
=9/10
1/2+1/6+1/12+…+1/[n*(n+1)]
=1-1/(n+1)

=1/1*2+1/2*3+1/3*4+……+1/9*10 =1-1/2+1/2-1/3+1/3-1/4+……+1/9-1/10 =1-1/10 =9/10