Write the Word or Phrase That Best Completes Each Statement $$1 + 3 + 3 ^ { 2 } + \ldots + 3 ^ { n - 1 } = \frac { 3 ^ { n } - 1 } { 2 }$$

question 79

Essay

Write the word or phrase that best completes each statement or answers the question.
Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.
- $$1 + 3 + 3 ^ { 2 } + \ldots + 3 ^ { n - 1 } = \frac { 3 ^ { n } - 1 } { 2 }$$

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Definitions:

Epigenetics

Differences in gene expression related to environment and experience.

Neurotrophic Factor

Neurotrophic factors are a family of proteins that are responsible for the growth, survival, and maintenance of neurons during development and in the adult nervous system.

Brain-derived

Pertaining to substances or factors that originate from the brain, such as brain-derived neurotrophic factor (BDNF) which supports neuron growth and survival.

Neural Plasticity

The ability of the nervous system to change and adapt, both in structure and function, in response to experiences or injuries.