查看完整版本: 请教1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+...+1/(2005*2006)=

请教1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+...+1/(2005*2006)=

请教1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+...+1/(2005*2006)=.

在线等答案，谢谢大家了！.

1/(2*3)=1/2-1/3
1/(3*4)=1/3-1/4

同理
可以得出,1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+...+1/(2005*2006)= 1-1/2006=2005/2006.

太谢谢了！.