1/10+1/40+1/88+1/154+1/238+1/340=
答案:4 悬赏:30 手机版
解决时间 2021-01-22 20:38
- 提问者网友：留有余香
- 2021-01-22 17:37
1/10+1/40+1/88+1/154+1/238+1/340=
最佳答案
- 五星知识达人网友：蓝房子
- 2021-01-22 17:54
1/10+1/40+1/88+1/154+1/238+1/340
=1/3×(3/10+3/40+3/88+3/154+3/238+3/340)
=1/3×(1/2-1/5+1/5-1/8+1/8-1/11+1/11-1/14+1/14-1/17+1/17-1/20)
=1/3×(1/2-1/20)
=1/3×9/20
=3/20
=1/3×(3/10+3/40+3/88+3/154+3/238+3/340)
=1/3×(1/2-1/5+1/5-1/8+1/8-1/11+1/11-1/14+1/14-1/17+1/17-1/20)
=1/3×(1/2-1/20)
=1/3×9/20
=3/20
全部回答
- 1楼网友：春色三分
- 2021-01-22 20:56
3/10+3/40+3/88+1/154+1/238+1/340 = (1/2 - 1/5) + (1/5 - 1/8) + (1/8 - 1/11) + (1/11 - 1/14)/3 + (1/14 - 1/17)/3 + (1/17 - 1/20)/3
= (1/2 - 1/11) + (1/11 - 1/20)/3
- 2楼网友：轻熟杀无赦
- 2021-01-22 19:39
10=2×5
40=5×8
88=8×11
154=11×14
238=14×17
340=17×20
∴可得：
3/10=(1/2)-(1/5)
3/40=(1/5)-(1/8)
3/88=(1/8)-(1/11)
...
3/340=(1/17)-(1/20)
累加，可得：
3S=(1/2)-(1/20)=9/20
S=3/20
- 3楼网友：十年萤火照君眠
- 2021-01-22 18:39
1/10+1/40+1/88+1/154+1/238+1/340
=1/(2×5)+1/(5×8)+1/(8×11)+1/(11×14)+1/(14×17)+1/(17×20)
=1/3×(1/2-1/5)+1/3(1/5-1/8)+1/3(1/8-1/11)+1/3(1/11-1/14)+1/3(1/14-1/17)+1/3(1/17-1/20)
=1/3(1/2-1/5+1/5-1/8+1/8-1/11+1/11-1/14+1/14-1/17+1/17-1/20)
=1/3×(1/2-1/20)
=3/20
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