1x2分之1+2x3分之1+3x4分之1...+n(n+1)分之1

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1x2分之1+2x3分之1+3x4分之1...+n(n+1)分之1

=1/1-1/2+1/2-1/3+1/3-1/4+...+1/(n-1)-1/n+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)

1x2分之1+2x3分之1+3x4分之1...+n(n+1)分之1
=1/1-1/2+1/2-1/3+1/3-1/4+...+1/(n-1)-1/n+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)