虎牙直播怎么设置弹幕:数学问题

这题很简单
把通式列出来,我们可以看出
这是一个数列的前100项和
这个数列的通项公式是
2/(n+1)n n是项数(因为每个数的分母都是一个公差=1首项是1的等差数列)
把整个这个数列提出一个2
1/(n+1)n = 1/n - 1/(n+1)
那么这个前100项和写成
2*(1- 1/2 + 1/2 - 1/3 .........- 1/101)
那么最后是2*(1-1/101)
=200/101

开始我说错了,对不住了啊

应该是200/101

1+2+3+……+n=n(n+1)/2
1/(1+2+3+4+…+N)=2/[n(n+1)]
故，
1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+……+1/(1+2+3+4+……+n)
=2/(1*2)+2/(2*3)+2/(3*4)+……+2/[n*(n+1)]
=2{1/(1*2)+1/(2*3)+1/(3*4)+……+1/[n*(n+1)]}
=2[1-1/2+1/2-1/3+1/3-1/4+……+1/n-1-1/(n+1)]
=2[1-1/(n+1)]
=2n/(n+1)

这里面用到了1/[n(n+1)]=1/n - 1/(n+1)

n==100代入，结果为200/101

+2+3+……+n=n(n+1)/2
1/(1+2+3+4+…+N)=2/[n(n+1)]
1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+……+1/(1+2+3+4+……+n)
=2/(1*2)+2/(2*3)+2/(3*4)+……+2/[n*(n+1)]
=2{1/(1*2)+1/(2*3)+1/(3*4)+……+1/[n*(n+1)]}
=2[1-1/2+1/2-1/3+1/3-1/4+……+1/n-1-1/(n+1)]
=2[1-1/(n+1)]
=2n/(n+1) 1/[n(n+1)]=1/n - 1/(n+1)
n=100代入，结果为200/101

1+2+3+……+n=n(n+1)/2
1/(1+2+3+4+…+N)=2/[n(n+1)]
故，
1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+……+1/(1+2+3+4+……+n)
=2/(1*2)+2/(2*3)+2/(3*4)+……+2/[n*(n+1)]
=2{1/(1*2)+1/(2*3)+1/(3*4)+……+1/[n*(n+1)]}
=2[1-1/2+1/2-1/3+1/3-1/4+……+1/n-1-1/(n+1)]
=2[1-1/(n+1)]
=2n/(n+1)

这里面用到了1/[n(n+1)]=1/n - 1/(n+1)

n=100代入，结果为200/101

1+2+3+……+n=n(n+1)/2
1/(1+2+3+4+…+N)=2/[n(n+1)]
故，
1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+……+1/(1+2+3+4+……+n)
=2/(1*2)+2/(2*3)+2/(3*4)+……+2/[n*(n+1)]
=2{1/(1*2)+1/(2*3)+1/(3*4)+……+1/[n*(n+1)]}
=2[1-1/2+1/2-1/3+1/3-1/4+……+1/n-1-1/(n+1)]
=2[1-1/(n+1)]
=2n/(n+1)

这里面用到了1/[n(n+1)]=1/n - 1/(n+1)

n=100代入，结果为200/101