Write the Word or Phrase That Best Completes Each Statement

Essay

Write the word or phrase that best completes each statement or answers the question.
Use mathematical induction to prove the following statement for all positive integers n.
- $$1 + \frac { 5 } { 7 } + \frac { 25 } { 49 } + \ldots + \left( \frac { 5 } { 7 } \right) ^ { n - 1 } = \frac { 7 } { 2 } \left[ 1 - \left( \frac { 5 } { 7 } \right) ^ { n } \right]$$