Determine Whether the Geometric Series Converges or Diverges $$- \frac { 1 } { 5 } + \frac { 1 } { 25 } - \frac { 1 } { 125 } + \frac { 1 } { 625 } - \cdots$$

question 144

Short Answer

Determine whether the geometric series converges or diverges. If it converges, find its sum.
$$- \frac { 1 } { 5 } + \frac { 1 } { 25 } - \frac { 1 } { 125 } + \frac { 1 } { 625 } - \cdots$$

---

Definitions:

Probability Calculus

A branch of mathematics that deals with calculating the likelihood of various outcomes.

Conjunction

A logical operator that connects two propositions or statements and requires both to be true in order for the whole conjunction to be true.

Probability Calculus

A branch of mathematics dealing with calculating the likelihood of various outcomes in uncertain situations.

Complex Event Probabilities

The calculation of the likelihood of outcomes that involve two or more independent events occurring.