Write the Word or Phrase That Best Completes Each Statement $$6 + 6 ^ { 2 } + \ldots + 6 ^ { n } = 6 \left( \frac { 6 ^ { n } - 1 } { 5 } \right)$$

question 131

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.
- $$6 + 6 ^ { 2 } + \ldots + 6 ^ { n } = 6 \left( \frac { 6 ^ { n } - 1 } { 5 } \right)$$

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Definitions:

Cash Dividend

A payment made by a corporation to its shareholders, usually in the form of cash.

Excess Cash

Funds that exceed the necessary operating and investment cash required by a business, often indicating potential for dividends, buybacks, or investments.