1/1*2+1/2*3+1/3*4+...+1/n(n+1)化简

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1/1*2+1/2*3+1/3*4+...+1/n(n+1)化简

1/1*2+1/2*3+1/3*4+...+1/n(n+1)化简
1/1*2+1/2*3+1/3*4+...+1/n(n+1)化简

1/1*2+1/2*3+1/3*4+...+1/n(n+1)化简
1/1*2+1/2*3+1/3*4+...+1/n(n+1)
=(1/1)-(1/2)+(1/2)-(1/3)+(1/3)-(1/4)+...+(1/n)-[1/(n+1)]
=1-1/(n+1)
=(n+1-1)/(n+1)
=n/(n+1).

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

1/1*2+1/2*3+1/3*4+...+1/n(n+1)=1-1/2+1/2-1/3+1/3-1/4+...+1/n-1/(n+1)=1-1/(n+1)
这类问题很常见的- -!

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