Question

计算题1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+......+1/101

急！！！！！！！！！！！！！！！！
原题1+1/（1+1）+1/（1+2）。。。。。。1/（1+100）

Answer 1

1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3...+n)
=1+1*2/(2*3)+1*2/(3*4)+...+1*2/[n*(1+n)]
=2[1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/n-1/(n+1)]
=2[1/2+1/2-1/(n+1)]
=2-2/(n+1)
=2n/(n+1)

我给你求出了通项公式 接下去你应该会了把

Answer 2

+1/(1+2)+1/(1+2+3)+...+1/(1+2+3...+n)
=1+1*2/(2*3)+1*2/(3*4)+...+1*2/[n*(1+n)]
=2[1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/n-1/(n+1)]
=2[1/2+1/2-1/(n+1)]
=2-2/(n+1)
=2n/(n+1)

Answer 3

=好难