Question

Use the given information to determine if the geometric series converges or
diverges. If it converges, find the sum.
ai = 0.75; r = 5
a) The series converges to 3.75.
b) The series converges to 0.15.
c) The series diverges. There is no sum.
d) The series converges to 20.

Answer 1

Answer:

c) The series diverges. There is no sum.

Step-by-step explanation:

A geometric series is a series of the form:

$S = \Sigma_{i=0}^{n} a\cdot r^{i}$, $\forall i \in \mathbb{N}_{O}$

Where:

$a$ - First term of the series, dimensionless.

$r$ - Common ratio, dimensionless.

A geometric series converges only if $|r| < 1$. As $r > 1$, the geometric series diverges. Hence, the right answer is C.