Determine the Sum, If It Exists, of the Infinite Geometric $4+\frac{4}{3}+\frac{4}{9}+\frac{4}{27}+\ldots$

question 75

Short Answer

Determine the sum, if it exists, of the infinite geometric series
$4+\frac{4}{3}+\frac{4}{9}+\frac{4}{27}+\ldots$

---

Definitions:

Free-rider Problem

A situation where individuals consume a good without contributing to its cost, typically in the context of public goods.

Public Good

A good or service offered to every member of a community for free, supplied by either governmental bodies or private entities without the intention of making a profit.

Optimal Level

The most efficient, beneficial, or favorable point in a process or activity, often associated with achieving the best outcome or maximum productivity.

Public Good

A good that is non-excludable and non-rivalrous, where one person's enjoyment of the good does not diminish the ability of others to enjoy it, typically provided by the government.