Question

Determine whether the infinite geometric series converges or diverges: (216 + 36 + 6 + ldots). If it converges, find its sum.

Answer 1

The infinite geometric series converges with a sum of 259.2.

Step-by-step explanation:

This is an infinite geometric series with a common ratio of 1/6. To determine if the series converges or diverges, we can use the formula for the sum of an infinite geometric series:

S = a / (1 - r)

Where S is the sum of the series, a is the first term, and r is the common ratio. In this case, a = 216 and r = 1/6:

S = 216 / (1 - 1/6)

Simplifying,

S = 216 / (6/6 - 1/6)

= 216 / (5/6)

= 216 * (6/5)

= 259.2

Therefore, the infinite geometric series converges with a sum of 259.2.