Find the sum of the convergent series.
Sigma (lower n = 0; upper infinity) 8*(4/5)^n
To find the sum of the convergent series, we can use the formula for the sum of an infinite geometric series.
The formula for the sum of an infinite geometric series is given by:
S = a / (1 - r),
where 'S' is the sum of the series, 'a' is the first term of the series, and 'r' is the common ratio between consecutive terms.
In this case, the first term (a) of the series is 8, and the common ratio (r) is (4/5).
Substituting these values into the formula, we can find the sum (S) of the series:
S = 8 / (1 - (4/5)).
Now, let's simplify the expression:
S = 8 / (1 - 4/5)
= 8 / (1/5)
= 8 * (5/1)
= 40.
Therefore, the sum of the given series is 40.