1/1X3+1/2X4+1/3X5……1/48X50=？
答案:3 悬赏:30 手机版
解决时间 2021-01-15 23:18
- 提问者网友：原来太熟悉了会陌生
- 2021-01-15 04:36
1/1X3+1/2X4+1/3X5……1/48X50=？
最佳答案
- 五星知识达人网友：鱼芗
- 2021-01-15 04:44
1/(1×3)+1/(2×4)+1/(3×5)+……+1/(48×50)
=[1/(1×3)+1/(3×5)+……+1/(47×49)]+[1/(2×4)+1/(4×6)+……+1/(48×50)]
=[1/2×(1-1/3)+1/2×(1/3-1/5)+……+1/2×(1/47-1/49)]+[1/2×(1/2-1/4)+1/2×(1/4-1/6)+……+1/2×(1/48-1/50)]
=1/2×(1-1/3+1/3-1/5+……+1/47-1/49)+1/2×(1/2-1/4+1/4-1/6+……+1/48-1/50)
=1/2×(1-1/49)+1/2×(1/2-1/50)
=1/2×48/49+1/2×12/25
=24/49+6/25
=600/1225+294/1225
=894/1225
=[1/(1×3)+1/(3×5)+……+1/(47×49)]+[1/(2×4)+1/(4×6)+……+1/(48×50)]
=[1/2×(1-1/3)+1/2×(1/3-1/5)+……+1/2×(1/47-1/49)]+[1/2×(1/2-1/4)+1/2×(1/4-1/6)+……+1/2×(1/48-1/50)]
=1/2×(1-1/3+1/3-1/5+……+1/47-1/49)+1/2×(1/2-1/4+1/4-1/6+……+1/48-1/50)
=1/2×(1-1/49)+1/2×(1/2-1/50)
=1/2×48/49+1/2×12/25
=24/49+6/25
=600/1225+294/1225
=894/1225
全部回答
- 1楼网友：鱼芗
- 2021-01-15 07:05
∵1/x×（x+2）=1/2×[1/x-1/（x+2）]
∴原式=1/2×（1-1/3）+1/2×（1/2-1/4）+……+1/2（1/47-1/49）+1/2（1/48-1/50）
=1/2×（1-1/3+1/2-1/4+1/3-1/5+……+1/47-1/49+1/48-1/50)
=1/2×(1+1/2-1/49-1/50)
=1788/2450=894/1225
∴原式=1/2×（1-1/3）+1/2×（1/2-1/4）+……+1/2（1/47-1/49）+1/2（1/48-1/50）
=1/2×（1-1/3+1/2-1/4+1/3-1/5+……+1/47-1/49+1/48-1/50)
=1/2×(1+1/2-1/49-1/50)
=1788/2450=894/1225
- 2楼网友：动情书生
- 2021-01-15 06:16
提醒你一下吧，一项分成两项1/1*3=1/2（1-1/3），1/2*4=1/2（1/2-1/4）你在继续试试吧，有规律的，你看看吧！追答如果不行再发图
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