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 whether the series converges or diverges.
$$\lim_{m	o\infty}\left|\frac{(-6)^{m+2}}{4^{8(m+1)}}\cdot\frac{4^{8m}}{(-6)^{m+1}}ight|=\lim_{m	o\infty}\frac{6}{4^8}=0<1$$
Since the limit is less than 1, by the ratio test, the series converges.

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 $\sum _ { m = 1 } ^ { \infty } \frac { ( - 6 ) ^ { m + 1 } } { 4 ^ { 8 m } }$