1/1*2+1/2*3+1/3*4+L+1/n(n+1)要写过程,加急啊

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1/1*2+1/2*3+1/3*4+L+1/n(n+1)要写过程,加急啊

1/1*2+1/2*3+1/3*4+L+1/n(n+1)要写过程,加急啊
1/1*2+1/2*3+1/3*4+L+1/n(n+1)要写过程,加急啊

1/1*2+1/2*3+1/3*4+L+1/n(n+1)要写过程,加急啊
1/1*2=1/1-1/2
1/2*3=1/2-1/3
1/n(n+1)=1/n-1/(n+1)
原式=1/1-1/2+1/2-1/3+1/3-1/4+...+1/n-1/(n+1)=1/1-1/(n+1)=n/(n+1)

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