1/n(n+1)+1/(n+1)(n+2)+1/(n+2)(n+3)+……+1/(n+2005)(n+2006)求出当n=1时,该代数式的值

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1/n(n+1)+1/(n+1)(n+2)+1/(n+2)(n+3)+……+1/(n+2005)(n+2006)求出当n=1时,该代数式的值
1/n(n+1)+1/(n+1)(n+2)+1/(n+2)(n+3)+……+1/(n+2005)(n+2006)求出当n=1时,该代数式的值

1/n(n+1)+1/(n+1)(n+2)+1/(n+2)(n+3)+……+1/(n+2005)(n+2006)求出当n=1时,该代数式的值
1/n(n+1)+1/(n+1)(n+2)+1/(n+2)(n+3)+……+1/(n+2005)(n+2006)=(1/n-1/n+1)+(1/n+1-1/n+2)+(1/n+2-1/n+3)+……+(1/n+2005-1/n+2006)=1/n-1/n+2006.
当n=1时,原式=1-(1/2007)=2006/2007

拆分法：1/n(n+1)=(1/n)-(1/n+1) 同理，这个代数式的和为：1/n - 1/(n+2006),代入n=?即可。

1/n(n+1)=(1/n)-(1/n+1),按照这样的方法把后面的每项都分解，合并后就得到原式=(1/n)-(1/n+2006).带入n就得到了。代数式的值为2006/2007

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