1+1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55+1/66+.+1/2021055

题目

1+1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55+1/66+.+1/2021055
是有点难,不过还是希望大家来帮我

答案

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
=4020/2011
1+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