Summation notation $ 1 + \frac{1}{1+2} + \frac{1}{1+2+3} + \ldots + \frac{1}{1+2+3 + \ldots +n} + \ldots $ How to write the sum
$$
 1 + \frac{1}{1+2} + \frac{1}{1+2+3} + \ldots + \frac{1}{1+2+3 + \ldots +n} + \ldots
  $$
in summation (∑) notation.There are 2 series here, one the entire 1 + (1/1+2)... series and the other one in denominator of each term. This summation is a sub-part of a Induction problem.

$$\sum_{i=1}^n \frac{1}{\sum_{j=1}^i j}$$
You can calculate $a_i=\sum_{j=1}^i j$ first, then represent $\frac{1}{a_i}=b_{i}-b_{i-1}$, then $\sum_{i=1}^n (b_i-b_{i-1})=b_n-b_0$.
