1+1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55+1/66+.+1/202105

这个要先提取公因数2,然后再进行裂项求和即可。1+1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55+1/66+。+1/2021055=2*(1/2+1/6+1/12+1/20+1/30+1/42+1/56+。1/4042110)=2*[(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+。(2010-1/2011）=2*[1- 1/2011 ] =2*2010/2011=4020/20111+1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55+1/66+。+1/2021055=1+2*(1/6+1/12+1/20+1/30+1/42+1/56+。1/4042110)=1+2*[(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+。(1/2010-1/2011）]=1+2*[1/2-1/2011]=1+1-2/2011=1又2009/2011