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:

World Population

The total number of human beings currently living on Earth, which is subject to change due to birth rates, death rates, and migration patterns.

Infant Mortality Rate

is a measure indicating the number of deaths of infants under one year of age per 1,000 live births in a given year, used as an important indicator of the health status of a population.

Gesellschaft

A term used in sociology to describe a society or group characterized by impersonal, formal relations and a focus on individual accomplishments.

Immigrants

People who move to a country other than their native country to live, often for reasons like employment, education, or escaping conflict.