Answer:
B
Step-by-step explanation:
A series is said to be convergent if |r| < 1. Where r is the common ratio of the series.
If |r| ≥ 1 then the geometric series diverges.
25/3+125/9+625+ ...
r = 125/9 ÷25/3 = 5/3
625/27 ÷ 125/9 = 5/3
In the series, r is greater than 1. So the series is divergent.
How much are each of the calculators?
Answer:
Absolutely convergent
0.82
Step-by-step explanation:
Use the alternating series test.
lim(n→∞) (1/√n) = 0
1/√n > 1/√(n+1) for n > 0
It is absolutely convergent.
Use error estimation.
1/(n+1)² < 0.01
(n+1)² > 100
n+1 > 10
n > 9
n = 10
Sum the first 10 terms.
∑₁¹⁰ (-1)ⁿ⁻¹/n²
= 1/1² − 1/2² + 1/3² − 1/4² + 1/5² − 1/6² + 1/7² − 1/8² + 1/9² − 1/10²
≈ 0.82
Answer:
<h3>
3.375 Bags</h3>
Step-by-step explanation:
Convert 9 into an improper fraction. Specifically 27/3. Then you would convert 2 2/3 into an improper fractions as well. To get 8/3. Next you will divide 27/3 by 8/3 to get 27/8. We get 27/8 because we end up multipliying 27/3 by the receprical of 8/3. Then if you simplify you get 3.375 as your answer.