Test the series for convergence or divergence. $$\sum _ { m - 1 } ^ { \infty } \frac { ( - 6 ) ^ { m + 1 } } { 4 ^ { 8 m } }$$
A) The series is convergent.
B) The series is divergent.

Question

Quizplus · Accepted Answer

We can use the ratio test to determine convergence or divergence: 
\begin{align*}
\lim_{m	o\infty}\left|\frac{(-6)^{m+2}}{4^{8(m+1)}}\cdot\frac{4^{8m}}{(-6)^{m+1}}ight| &= \lim_{m	o\infty}\frac{36}{4^8}\
&=\frac{36}{65536}<1
\end{align*}
Since the limit is less than 1, the series converges by the ratio test.

Test the Series for Convergence or Divergence ∑m−1∞(−6)m+148m\sum _ { m - 1 } ^ { \infty } \frac { ( - 6 ) ^ { m + 1 } } { 4 ^ { 8 m } }m−1∑∞​48m(−6)m+1​

Test the Series for Convergence or Divergence $\sum _ { m - 1 } ^ { \infty } \frac { ( - 6 ) ^ { m + 1 } } { 4 ^ { 8 m } }$