Determine if the infinite geometric series converges or diverges. If the series converges, find its sum.
-$$\sum _ { i = 1 } ^ { \infty } \frac { 1 } { 5 } ( 4 ) ^ { \mathrm { i } } - 1$$
A) converges, 8
B) converges, $\frac { 4 } { 5 }$
C) converges, $\infty$
D) diverges

Question

Quizplus · Accepted Answer

The given series is divergent because the common ratio $r = 4 > 1$, and for a geometric series to converge, the absolute value of the common ratio must be less than 1.

Determine If the Infinite Geometric Series Converges or Diverges ∑i=1∞15(4)i−1\sum _ { i = 1 } ^ { \infty } \frac { 1 } { 5 } ( 4 ) ^ { \mathrm { i } } - 1i=1∑∞​51​(4)i−1

Determine If the Infinite Geometric Series Converges or Diverges $\sum _ { i = 1 } ^ { \infty } \frac { 1 } { 5 } ( 4 ) ^ { \mathrm { i } } - 1$