Find the sum of the infinite geometric series given by ∑_(k=1)^∞〖(2/9)^k〗

Isn't the sum equal to

ar/(1-r) ?

http://en.wikipedia.org/wiki/Geometric_progression

To find the sum of an infinite geometric series, you can use the formula:

S = a / (1 - r),

where S represents the sum of the series, a is the first term, and r is the common ratio.

In this case, the first term (a) is (2/9)^1 = 2/9, and the common ratio (r) is (2/9).

Now, substitute these values into the formula:

S = (2/9) / (1 - 2/9).

To simplify, multiply the numerator and denominator of the right side by 9:

S = (2/9) * (9/7) = 2/7.

So, the sum of the infinite geometric series given by ∑_(k=1)^∞〖(2/9)^k〗 is 2/7.