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

学习时间:2026-05-30 14:02:31 阅读：8953

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

优秀的蜗牛

2026-05-30 14:02:31



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