Determine the Convergence or Divergence of the Following Series $\sum _ { n = 0 } ^ { \infty } \frac { 4 } { 2 ^ { n } }$

question 12

Multiple Choice

Determine the convergence or divergence of the following series. Use a symbolic algebra utility to verify your result. $\sum _ { n = 0 } ^ { \infty } \frac { 4 } { 2 ^ { n } }$

• A)The series diverges.
• B)The series converges.

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Definitions:

Truth-Functional Compound

In logic, a statement which is formed by combining simpler statements and whose truth is determined entirely by the truth values of these simpler statements.

Quantifier

A symbol or phrase in formal logic used to specify the quantity of specimens in the domain of discourse that satisfy an open formula.

Open Sentences

Statements in mathematics containing one or more variables, whose truth or falsity can vary depending on the values of these variables.

Scope

The portion of a statement in symbolic notation that is governed by a quantifier.