Chapter 12.4, Problem 31AE

Use mathematical induction to prove that

$a\text{ + }\left(a\text{ + }d\right)\text{ + }\left(a\text{ + 2}d\right)\text{ + }\cdot \cdot \cdot \text{ + }\left[a\text{ + }\left(n-1\right)d\right]\text{ = }na\text{ + }d\frac{n\left(n-1\right)}{2}$