Math Problem Solver

The sum of the series to its nth term is given by: \[S_n=\frac{n \left(n^{2} + 3 n + 2\right)}{6}\]

This is an arithmetic series.

The explicit formula for the nth term of this series is: \[a_n = \frac{n \left(n + 1\right)}{2}\]Use this to find the summation formula: $$\begin{aligned}S_n&=\sum_{i=1}^{n} a_{i} \\ &=\sum_{i=1}^{n} \frac{i \left(i + 1\right)}{2} \\ &=\frac{n \left(n^{2} + 3 n + 2\right)}{6} \end{aligned}$$ Note: Replace all $n$ in $a_n$ in the summation with $i$.