1/1+（2/1-1/2）+（3/1-2/2+1/3）+（4/1-3/2+2/3-1/4）+。。。+（9/1-8
答案:2 悬赏:20 手机版
解决时间 2021-11-22 17:46
- 提问者网友：無理詩人
- 2021-11-22 13:41
1/1+（2/1-1/2）+（3/1-2/2+1/3）+（4/1-3/2+2/3-1/4）+。。。+（9/1-8/2+7/3-6/4+。。。+3/7-2/8+1/9
最佳答案
- 五星知识达人网友：零点过十分
- 2021-11-22 15:20
原式
= (1+2+3+...+9)/1 - (1+2+3+...+8)/2 + (1+2+3+...+7)/3 - (1+2+3+...+6)/4 +……+ 1/9
= 45/1 - 36/2 + 28/3 - 21/4 + 15/5 - 10/6 + 6/7 - 3/8 + 1/9
= 45 - 18 + 28/3 - 21/4 + 3 - 5/3 + 6/7 - 3/8 + 1/9
= (45-18+3) + (28/3-5/3) -(21/4+3/8) + 6/7 + 1/9
= 30 + (7+2/3) -(5+5/8) + (1-1/7) + 1/9
= (30+7-5+1) + (2/3-5/8-1/7+1/9)
= 33 + (336-315-72+56)/504
= 33又5/504
= (1+2+3+...+9)/1 - (1+2+3+...+8)/2 + (1+2+3+...+7)/3 - (1+2+3+...+6)/4 +……+ 1/9
= 45/1 - 36/2 + 28/3 - 21/4 + 15/5 - 10/6 + 6/7 - 3/8 + 1/9
= 45 - 18 + 28/3 - 21/4 + 3 - 5/3 + 6/7 - 3/8 + 1/9
= (45-18+3) + (28/3-5/3) -(21/4+3/8) + 6/7 + 1/9
= 30 + (7+2/3) -(5+5/8) + (1-1/7) + 1/9
= (30+7-5+1) + (2/3-5/8-1/7+1/9)
= 33 + (336-315-72+56)/504
= 33又5/504
全部回答
- 1楼网友：独行浪子会拥风
- 2021-11-22 16:57
原式
= (1+2+3+...+9)/1 - (1+2+3+...+8)/2 + (1+2+3+...+7)/3 - (1+2+3+...+6)/4 +……+ 1/9
= 45/1 - 36/2 + 28/3 - 21/4 + 15/5 - 10/6 + 6/7 - 3/8 + 1/9
= 45 - 18 + 28/3 - 21/4 + 3 - 5/3 + 6/7 - 3/8 + 1/9
= (45-18+3) + (28/3-5/3) -(21/4+3/8) + 6/7 + 1/9
= 30 + (7+2/3) -(5+5/8) + (1-1/7) + 1/9
= (30+7-5+1) + (2/3-5/8-1/7+1/9)
= 33 + (336-315-72+56)/504
= 33又5/504
= (1+2+3+...+9)/1 - (1+2+3+...+8)/2 + (1+2+3+...+7)/3 - (1+2+3+...+6)/4 +……+ 1/9
= 45/1 - 36/2 + 28/3 - 21/4 + 15/5 - 10/6 + 6/7 - 3/8 + 1/9
= 45 - 18 + 28/3 - 21/4 + 3 - 5/3 + 6/7 - 3/8 + 1/9
= (45-18+3) + (28/3-5/3) -(21/4+3/8) + 6/7 + 1/9
= 30 + (7+2/3) -(5+5/8) + (1-1/7) + 1/9
= (30+7-5+1) + (2/3-5/8-1/7+1/9)
= 33 + (336-315-72+56)/504
= 33又5/504
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