1\3+1\6+1\10+1\15+1\21+1\28+1\36+1\45+1\50+1\55

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/12 08:50:34

1\3+1\6+1\10+1\15+1\21+1\28+1\36+1\45+1\50+1\55
请写清过程,不要省略

先提取公因数2,然后再进行裂项求和即可.
原式=2*(1/6+1/12+1/20+1/30.+1/110+1/100)
=2*[(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+.+(1/10-1/11)+1/100]
=2*[1/2-1/11+1/100] 消去中间项
=2*461/1100
=461/550
再问：为什么？看不懂哎怎么得数又变了
再答：我再写详细点！稍等！因为1/6=1/2-1/3，1/12=1/3-1/4，1/20=1/4-1/5,1/42=1/6-1/7…… 原式=2*(1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/100+1/110) =2*(1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/100) =2(1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11+1/100) =2*(1/2-1/11+1/100) 消去中间项 =2*461/1100 =461/550 我发觉1/100无法消去，如果题目没有抄错就是上面的结果。之前看漏了1/50，所以算的是： 1\3+1\6+1\10+1\15+1\21+1\28+1\36+1\45+1\55 =2*(1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110) =2*(1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110) =2(1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11) =2*(1/2-1/11) 消去中间项 =2*9/22 =9/11 不明白可追问！请采纳！谢谢！

1\3+1\6+1\10+1\15+1\21+1\28+1\36+1\45+1\50+1\55 1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55+1/66 1/3 + 1/6 + 1/10 + 1/15 + 1/21 + 1/28 + 1/36 + 1/45 + 1/55=? 1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/50+1/55=? 1\3+1\6+1\10+1\15+1\21+1\28+1\36+1\45+1\55+1\66+1\78+1\91+1\ 1+1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55+1/66+.+1/202105 1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55+1/66+1/78+1/91 1/3+1/8+1/10+1/15+1/21+1/28+1/36+1/45+1/55 【急】!简便运算!(1) 1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55+1/66 计算：1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55+1/66+q/78+1/91 奥数数学题1+1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55简便运算急~ 小六计算题1+1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55=?如果把他都改成-号