1—1／2+1／6+1／12+1／20+......+1／72+1／90
答案:4 悬赏:60 手机版
解决时间 2021-03-16 15:58
- 提问者网友：刺鸟
- 2021-03-16 03:48
1—1／2+1／6+1／12+1／20+......+1／72+1／90
最佳答案
- 五星知识达人网友：独钓一江月
- 2021-03-16 04:47
原式=1-1/2+1/2*3+1/3*4+……+1/9*10
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/9-1/10)
=1-1/10
=9/10
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/9-1/10)
=1-1/10
=9/10
全部回答
- 1楼网友：舊物识亽
- 2021-03-16 07:47
解：原式=
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)+1/(8*9)+1/(9*10)
=1-1/2+(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)
=1-1/10 （打开括号）
=9/10
注：1/n(n+1) =1/n-1/(n+1)
- 2楼网友：风格不统一
- 2021-03-16 07:22
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
＝1-1/2+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
=1-1/10
=9/10
- 3楼网友：拾荒鲤
- 2021-03-16 06:14
1—1／2+1／6+1／12+1／20+......+1／72+1／90
=1-1+1/2+1/2-1/3+1/3-1/4+...+1/9-1/10
=1-1/10
=9/10
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