Chapter 4.2, Problem 78E

Proof Prove each formula by mathematical induction. (You may need to review the method of proof by induction from a precalculus text.)

(a) ${\displaystyle \underset{i=1}{\overset{n}{\sum }}2i=n(n+1)}$ (b) ${\displaystyle \underset{i=1}{\overset{n}{\sum }}{i}^3=\frac{n^3{(n+1)}^2}{4}}$