Use the Principle of Mathematical Induction to Show That the Statement

question 105

Essay

Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.
- $$3 + 3 \cdot \frac { 1 } { 7 } + 3 \cdot \left( \frac { 1 } { 7 } \right) ^ { 2 } + \ldots + 3 \cdot \left( \frac { 1 } { 7 } \right) ^ { n - 1 } = \frac { 3 \left( 1 - \left( \frac { 1 } { 7 } \right) ^ { n } \right) } { 1 - \frac { 1 } { 7 } }$$

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Definitions:

Grana

Stacked membranous structures within chloroplasts that contain chlorophyll, where the light-dependent reactions of photosynthesis occur.

Photosynthesis

A process by which green plants and some other organisms use sunlight to synthesize foods from carbon dioxide and water. Photosynthesis in plants generally involves the green pigment chlorophyll and generates oxygen as a by-product.

Oxygen Atoms

Fundamental components of molecules, essential for respiration in organisms and a key element in the Earth's atmosphere.

Proton Gradient

The gradient of hydrogen ions (protons) across a membrane, which is a form of potential energy used for ATP production in cells.