Question

Find the sum of the infinite geometric series.
72+24+8+8/3+8/9+⋯

Answer 1

The sum of the infinite geometric series 72 + 24 + 8 + 8/3 + 8/9 + … is 108, calculated using the formula for an infinite geometric series sum.

Step-by-step explanation:

You are asking for the sum of an infinite geometric series. To find the sum of this series, we first need to identify the first term (a) and the common ratio (r). In the series you've provided, the first term, a, is 72. To find the common ratio, r, we divide the second term by the first term, which is 24/72 = 1/3. Since |r| < 1, this series converges and we can use the formula for the sum of an infinite geometric series:

S = a / (1 - r)

Substituting the values of a and r into the formula gives us:

S = 72 / (1 - 1/3) = 72 / (2/3) = 72 * (3/2) = 108

So, the sum of the infinite geometric series is 108.