# Math Help - Serious Series Problem

1. ## Serious Series Problem

What is the sum of:

1/1 + 1/(1+2) + 1/(1+2+3) + 1/(1+2+3+4) + ... + 1/(1+2+3+...+n)

2. Originally Posted by bearej50
What is the sum of:

1/1 + 1/(1+2) + 1/(1+2+3) + 1/(1+2+3+4) + ... + 1/(1+2+3+...+n)
$\sum_{k=1}^{j}k=\frac{j(j+1)}{2}$. And so $\sum_{j=1}^{n}\frac{1}{\sum_{k=1}^{j}k}=\sum_{j=1} ^{n}\frac{2}{j(j+1)}=2\sum_{j=1}^{n}\left\{\frac{1 }{j}-\frac{1}{j+1}\right\}=2\left[1-\frac{1}{n+1}\right]$.