Use Mathematical Induction to Prove That the Statement Is True $$2 + 5 + 8 + \ldots + ( 3 n - 1 ) = \frac { n ( 3 n + 1 ) } { 2 }$$

question 38

Essay

Use mathematical induction to prove that the statement is true for every positive integer n.
- $$2 + 5 + 8 + \ldots + ( 3 n - 1 ) = \frac { n ( 3 n + 1 ) } { 2 }$$

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Definitions:

Resting State

A term often used in neuroscience to describe the brain's activity when not focused on performing tasks or activities, providing insights into default network functions.

Cell Membrane

The semipermeable membrane surrounding the cytoplasm of a cell, which regulates the passage of substances in and out of the cell.

Resting Potential

The state of a neuron when it is not being stimulated or activated; it is the electrical potential of a neuron's interior relative to its surroundings when the neuron is not transmitting a signal.

Inactive Neuron

A neuron that is not currently firing or transmitting information.