1/3+1/(1+2)(3+2)+1/(1+4)(3+4)+.1/(1+2008)*(3+2008)

学习时间:2026-04-04 18:53:07 阅读：9924

1/3+1/(1+2)*(3+2)+1/(1+4)*(3+4)+.1/(1+2008)*(3+2008)

自由的黑裤

2026-04-04 18:53:07

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原式=1/(1*3)+1/(3*5)+1/(5*7)+。。。+1/(2009*2011)=1/2*(1-1/3+1/3-1/5+1/5-1/7+。。。+1/2009-1/2011)=1/2*(1-1/2011)=1/2*2010/2011=1005/2011