I'm reading Concrete Mathematics and trying to understand some of the equations. In particular how the author arrives to a particular solution.
Given: $$L_n = \frac{n(n+1)}{2} + 1$$ the author arrives to this solution for $L_{n-1}$:
$$L_n = L_{n-1} + n = \left(\frac{(n-1)n}{2}+1\right)+n = \frac{n(n+1)}{2}+1.$$
I understand how he arrives to $\left(\frac{(n-1)n}{2}+1\right)+n$, but cannot mathematically understand how he reduces that to the final solution $\frac{n(n+1)}{2}+1$.
Hint: $\left(\frac{(n-1)n}{2}+1\right)+n=\left(\frac{(n-1)n}{2}+n\right)+1=\frac{(n-1)n+2n}{2}+1=...?$