Use Mathematical Induction to Prove the Given Statement for All $$1 + 4 + 4 ^ { 2 } + 4 ^ { 3 } + \ldots + 4 ^ { n - 1 } = \frac { 4 ^ { n } - 1 } { 3 }$$

question 28

Short Answer

Use mathematical induction to prove the given statement for all positive integers n.
- $$1 + 4 + 4 ^ { 2 } + 4 ^ { 3 } + \ldots + 4 ^ { n - 1 } = \frac { 4 ^ { n } - 1 } { 3 }$$

Understand the concept and examples of institutional discrimination.

Distinguish between racism, prejudice, and discrimination.

Recognize the systemic nature of racism and its impact on societal structures.

Identify historical and contemporary examples of racist beliefs and their justifications.

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Definitions:

Gas Law

A set of laws that describe the behavior of gases in relation to pressure, volume, temperature, and quantity.

Mole

A mole is a unit of measurement used in chemistry to quantify the amount of substance, equivalent to approximately 6.022 x 10^23 particles, atoms, molecules, ions, or electrons.

Gas

One of the four fundamental states of matter with indefinite shape and volume, composed of molecules in constant random motion.

Gas Law

Mathematical relationships that describe the behavior of gases, relating pressure, volume, temperature, and amount of gas.