Did i answer correctly?
Find the sum of each infinite geometric series.
14. 4 + 2 + 1 + …
= 8
16. 1 + ½ + ¼ + …
= 2
18. 16 + 1.6 + .16 + …
17.7
The first two are correct,
the last one is off
16 + 1.6 + .16 + …
a = 16
r = 1/10
sum of all = a/(1-r) = 16/(1-1/10) = 16/(9/10)
= 160/9
17.7 is the rounded answer to the correct answer of 160/9
To find the sum of an infinite geometric series, you can use the formula:
S = a / (1 - r)
Where:
- S is the sum of the series,
- a is the first term of the series,
- r is the common ratio between consecutive terms.
Let's apply this formula to each of the given series:
14. 4 + 2 + 1 + ...
In this series, the first term (a) is 4, and the common ratio (r) between consecutive terms is 0.5 (2/4 = 1/2).
Using the formula, we get:
S = 4 / (1 - 0.5)
S = 8
So, the sum of the infinite geometric series is 8. Your answer is correct.
16. 1 + 1/2 + 1/4 + ...
In this series, the first term (a) is 1, and the common ratio (r) between consecutive terms is 0.5 (1/2 = 0.5).
Using the formula, we get:
S = 1 / (1 - 0.5)
S = 2
So, the sum of the infinite geometric series is 2. Your answer is correct.
18. 16 + 1.6 + 0.16 + ...
In this series, the first term (a) is 16, and the common ratio (r) between consecutive terms is also 0.1 (1.6/16 = 0.1).
Using the formula, we get:
S = 16 / (1 - 0.1)
S = 16 / 0.9
S ≈ 17.778
So, the sum of the infinite geometric series is approximately 17.778. Your answer is incorrect. The correct sum is approximately 17.778, not 17.7.