计算:1/a(a+1)+1/(a+1)(a+2)+...+1/(a+2006)(a+2007)快啊,等着救命聂!

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计算:1/a(a+1)+1/(a+1)(a+2)+...+1/(a+2006)(a+2007)快啊,等着救命聂!计算:1/a(a+1)+1/(a+1)(a+2)+...+1/(a+2006)(a+20

计算:1/a(a+1)+1/(a+1)(a+2)+...+1/(a+2006)(a+2007)快啊,等着救命聂!
计算:1/a(a+1)+1/(a+1)(a+2)+...+1/(a+2006)(a+2007)
快啊,等着救命聂!

计算:1/a(a+1)+1/(a+1)(a+2)+...+1/(a+2006)(a+2007)快啊,等着救命聂!
裂项:1/a(a+1)=1/a-1/(a+1)
1/a(a+1)+1/(a+1)(a+2)+...+1/(a+2006)(a+2007)
=1/a-1/(a+1)+1/(a+1)-1/(a+2)+...+1/(a+2006)-1/(a+2007)
=1/a-1/(a+2007)