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
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/23 19:54:49
![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](/uploads/image/z/69357-21-7.jpg?t=1%2B1%2F3%2B1%2F6%2B1%2F10%2B1%2F15%2B1%2F21%2B1%2F28%2B1%2F36%2B1%2F45%2B1%2F55%2B1%2F66%2B.%2B1%2F2021055%E6%98%AF%E6%9C%89%E7%82%B9%E9%9A%BE%2C%E4%B8%8D%E8%BF%87%E8%BF%98%E6%98%AF%E5%B8%8C%E6%9C%9B%E5%A4%A7%E5%AE%B6%E6%9D%A5%E5%B8%AE%E6%88%91)
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
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
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
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
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+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+1/15+1/42+......+1/4042110)
=2*(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5......+1/2010-1/2011)
=2*(1-1/2011)
=2*2010/2011
=4020/2011