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:

PGAL

Phosphoglyceraldehyde, an intermediate molecule formed in the photosynthesis and glycolysis metabolic pathways, important in the metabolic process.

NADPH

Nicotinamide adenine dinucleotide phosphate, a coenzyme involved in cellular processes, mainly anabolism and as a reducing agent in anabolic reactions.

Phosphate Group

A chemical group consisting of phosphorus bonded to four oxygen atoms, important in energy transfer.