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.

Question

Quizplus · Accepted Answer

This series is a geometric series with the first term $a = \frac{4}{2^0} = 4$ and common ratio $r = \frac{1}{2}$. Since the absolute value of the common ratio is less than 1 ($|r| = \frac{1}{2} < 1$), the series converges.

Determine the Convergence or Divergence of the Following Series ∑n=0∞42n\sum _ { n = 0 } ^ { \infty } \frac { 4 } { 2 ^ { n } }∑n=0∞​2n4​

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