Can you find the sum of the infinite geometric series $4+12+36+\cdots$ ? Why or Why not?
A) No. This is not a geometric series.
B) No. The common ratio, $r$, is greater than 1 .
C) Yes. This is a geometric series.
D) Yes. The common ratio, $r$, is less than 1 .

Question

Quizplus · Accepted Answer

The series is a geometric series with a common ratio $r = 3$ (since each term is obtained by multiplying the previous term by 3). The sum of an infinite geometric series can be found using the formula $S = \frac{a}{1 - r}$ if and only if $|r| < 1$. Since the common ratio here is greater than 1, the series does not converge, and its sum cannot be found.

Can You Find the Sum of the Infinite Geometric Series 4+12+36+⋯4+12+36+\cdots4+12+36+⋯

Can You Find the Sum of the Infinite Geometric Series $4+12+36+\cdots$