1/(1乘3)加1/(2乘4)加.....加1/(2015乘2017)
答案:2 悬赏:30
解决时间 2021-11-26 05:24
- 提问者网友：熱戀丶瘋
- 2021-11-25 04:41
1/(1乘3)加1/(2乘4)加.....加1/(2015乘2017)
最佳答案
- 二级知识专家网友：开心就好
- 2021-11-25 05:44
解原式
=1/2(1/1-1/3)+1/2(1/2-1/4)+.......+1/2(1/2015-1/2017)
=1/2[(1/1-1/3)+(1/2-1/4)+(1/3-1/5)+.....+(1/2014-1/2015)+(1/2015-1/2017)]
=1/2(1/1+1/2-1/2015-1/2017)
=1/2(3/2-1/2015-1/2017)
=1/2(1/1-1/3)+1/2(1/2-1/4)+.......+1/2(1/2015-1/2017)
=1/2[(1/1-1/3)+(1/2-1/4)+(1/3-1/5)+.....+(1/2014-1/2015)+(1/2015-1/2017)]
=1/2(1/1+1/2-1/2015-1/2017)
=1/2(3/2-1/2015-1/2017)
全部回答
- 1楼网友：ー何必说爱
- 2021-11-25 07:04
1*2+2*3+3*4+……+n(n+1)
=(1^2+1)+(2^2+2)+(3^2+3)+……+(n^2+n)
=(1^2+2^2+3^3+……+n^2)+(1+2+3+……+n)
=n(n+1)(2n+1)/6+n(n+1)/2
=n(n+1)(n/3+1/6+1/2)
=n(n+1)(n/3+2/3)
=n(n+1)(n+2)/3
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