Question

1/1x3+1/2x4+1/3x5.1/18x20=?简便算法,

Answer 1

1/n(n+2)=[1/n-1/(n+2)]/2

1/1*3+1/2*4+1/3*5+...+1/18*20

=[(1-1/3)+(1/2-1/4)+(1/3-1/5)+...+(1/18-1/20)]/2

=[1+1/2-1/19-1/20]/2

=531/760

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