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

question 195

Short Answer

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

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Definitions:

Intrinsic Value

The inherent, actual value of an asset, independent of its market value.

Underwater

A situation where the market value of an asset is less than the amount owed on it, often used in reference to mortgages.

Expiration Date

The last day on which an option or futures contract is valid or can be exercised.

Option

A financial derivative that gives the buyer the right, but not the obligation, to buy or sell an underlying asset at an agreed-upon price within a specific timeframe.