Question

Determine whether the infinite geometric series is convergent or divergent 1+1/3+1/9+1/27

Answer 1

To determine if the infinite geometric series 1 + 1/3 + 1/9 + 1/27 + ... converges or diverges, we can use the formula for the sum of an infinite geometric series: S = a / (1 - r), where "a" is the first term of the series and "r" is the common ratio.

In this case, the first term "a" is 1 and the common ratio "r" is 1/3. Plugging these values into the formula, we get:

S = 1 / (1 - 1/3) = 1 / (2/3) = 3/2

Since the sum of the infinite geometric series is a finite number (3/2), we can conclude that the series converges.