Use the Principle of Mathematical Induction to Show That the Statement

question 105

Essay

Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.
- $$3 + 3 \cdot \frac { 1 } { 7 } + 3 \cdot \left( \frac { 1 } { 7 } \right) ^ { 2 } + \ldots + 3 \cdot \left( \frac { 1 } { 7 } \right) ^ { n - 1 } = \frac { 3 \left( 1 - \left( \frac { 1 } { 7 } \right) ^ { n } \right) } { 1 - \frac { 1 } { 7 } }$$

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