Use Mathematical Induction to Prove That the Statement Is True

question 311

Essay

Use mathematical induction to prove that the statement is true for every positive integer n.
- $$4 + 4 \cdot \frac { 1 } { 8 } + 4 \cdot \left( \frac { 1 } { 8 } \right) ^ { 2 } + \ldots + 4 \cdot \left( \frac { 1 } { 8 } \right) ^ { n - 1 } = \frac { 4 \left( 1 - \left( \frac { 1 } { 8 } \right) ^ { n } \right) } { 1 - \frac { 1 } { 8 } }$$

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Definitions:

NAV

Net asset value, calculated as the total value of a fund's assets minus its liabilities, usually applied to mutual funds.

Offering Prices

The price at which new issues of stock, bonds, or other securities are made available for sale to the public for the first time.

Diversification

An investment strategy aimed at reducing risk by allocating investments across various financial instruments, industries, or other categories.

Professional Management

The process of overseeing and handling investment portfolios by experts or specialized firms to achieve specified investment objectives.