Determine the convergence or divergence of the series. $$\sum _ { n = 0 } ^ { \infty } \left( \frac { 1 } { 4 } \right) ^ { n }$$
A) converges
B) diverges
C) cannot be determined

Question

Quizplus · Accepted Answer

This is a geometric series with first term $a=1$ and common ratio $r=\frac{1}{4}$. Thus, the series converges to $\frac{a}{1-r}=\frac{1}{1-\frac{1}{4}}=\frac{4}{3}$.

Determine the Convergence or Divergence of the Series ∑n=0∞(14)n\sum _ { n = 0 } ^ { \infty } \left( \frac { 1 } { 4 } \right) ^ { n }n=0∑∞​(41​)n

Determine the Convergence or Divergence of the Series $\sum _ { n = 0 } ^ { \infty } \left( \frac { 1 } { 4 } \right) ^ { n }$