Determine the Sum of the Following Geometric Series $\frac { 2 ^ { 2 } } { 5 ^ { 3 } }$

question 126

Short Answer

Determine the sum of the following geometric series: $\frac { 2 ^ { 2 } } { 5 ^ { 3 } }$ + $\frac { 2 ^ { 4 } } { 5 ^ { 5 } }$ + $\frac { 2 ^ { 6 } } { 5 ^ { 7 } }$ + $\frac { 2 ^ { 8 } } { 5 ^ { 9 } }$ + $\frac { 210 } { 5 ^ { 11 } }$ + ... .
Enter just a reduced fraction of form $\frac { a } { b }$ .

---

Definitions:

Incarceration Rates

The proportion of a population that is confined in prison or jail, often expressed per 100,000 individuals.

Crime Rates

The frequency or number of criminal offenses recorded in a given area or population within a specified period of time.

Climate Change

The long-term alteration of temperature and typical weather patterns in a place, often attributed to human activity.

Politicized

A situation or process whereby an issue, policy, or action becomes heavily influenced or dictated by political considerations.