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.