Use Mathematical Induction to Prove That the Statement Is True $$4 + \frac { 4 } { 5 } + \frac { 4 } { 25 } + \ldots + \frac { 4 } { 5 ^ { n - 1 } } = 5 \left( 1 - \frac { 1 } { 5 ^ { n } } \right)$$

Essay

Use mathematical induction to prove that the statement is true for every positive integer n.
- $$4 + \frac { 4 } { 5 } + \frac { 4 } { 25 } + \ldots + \frac { 4 } { 5 ^ { n - 1 } } = 5 \left( 1 - \frac { 1 } { 5 ^ { n } } \right)$$