1/2+1/6+1/12+1/20+1/30+……+1/n(n+1)=2016/2017
供稿:hz-xin.com 日期:2024-04-19
1/2+1/6+1/12+1/20,前30个数的和为多少
=1/1-1/2+(1/2-1/3)+(1/3-1/4)+(1/5-1/6)+...+(1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)
第2016项 是 1/2016*2017,
前 2016项的和=2016/2017
前30个数的和为30/31
1/2+1/6+1/12+1/20+......
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+......+(1/30-1/31)
=1-1/31
=30/31
图
=1/1-1/2+(1/2-1/3)+(1/3-1/4)+(1/5-1/6)+...+(1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)
第2016项 是 1/2016*2017,
前 2016项的和=2016/2017