Question

Determine whether the geometric series 36 + 39.6 + 43.56 + ... converges or diverges, and identify the sum if it exists.

Answer 1

Answer:

Diverges

There is no sum.

Step-by-step explanation:

A geometric series has a general formula of:

$\sum ar^n$

Where 'a' is the initial term, 'n' is the number of terms, and 'r' is the constant ratio. If |r| < 1 than the series converges, but if |r| > 1, than the series diverges.

In this problem, the initial term is a = 36, the ratio can be found by:

$r = \frac{39.6}{36}=\frac{43.56}{39.6}\\ r=1.1$

Since the ratio is r =1.1 and 1.1 > 1.0, the series diverges.

In a diverging series, it is not possible to determine the sum of infinite terms, since it would be infinite.