Use Mathematical Induction to Prove That the Statement Is True

question 56

Essay

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

---

Definitions:

States

Conditions or situations that something can be in, often used in contexts like software states or physical states of matter.

Pull-in Current

The minimum current required to activate or "pull-in" a device, such as a relay or solenoid.

Actuate

To put into motion or action, typically referring to the operation of a mechanical device or system.

Applied Voltage

The voltage that is applied across a component or circuit, initiating its operation or influencing its performance.