Use Mathematical Induction to Prove the Given Statement for All $$\frac { 2 } { 3 } + \frac { 2 } { 9 } + \frac { 2 } { 27 } + \ldots + \frac { 2 } { 3 ^ { n } } = 1 - \left( \frac { 1 } { 3 } \right) ^ { n }$$

Short Answer

Use mathematical induction to prove the given statement for all positive integers n.
- $$\frac { 2 } { 3 } + \frac { 2 } { 9 } + \frac { 2 } { 27 } + \ldots + \frac { 2 } { 3 ^ { n } } = 1 - \left( \frac { 1 } { 3 } \right) ^ { n }$$