Answer:
a) -7/9
b) 16 / (n² + 15n + 56)
c) 1
Step-by-step explanation:
When n = 1, there is only one term in the series, so a₁ = s₁.
a₁ = (1 − 8) / (1 + 8)
a₁ = -7/9
The sum of the first n terms is equal to the sum of the first n−1 terms plus the nth term.
sₙ = sₙ₋₁ + aₙ
(n − 8) / (n + 8) = (n − 1 − 8) / (n − 1 + 8) + aₙ
(n − 8) / (n + 8) = (n − 9) / (n + 7) + aₙ
aₙ = (n − 8) / (n + 8) − (n − 9) / (n + 7)
If you wish, you can simplify by finding the common denominator.
aₙ = [(n − 8) (n + 7) − (n − 9) (n + 8)] / [(n + 8) (n + 7)]
aₙ = [n² − n − 56 − (n² − n − 72)] / (n² + 15n + 56)
aₙ = 16 / (n² + 15n + 56)
The infinite sum is:
∑₁°° aₙ = lim(n→∞) sₙ
∑₁°° aₙ = lim(n→∞) (n − 8) / (n + 8)
∑₁°° aₙ = 1
Answer:
2005400sblackwell
2005400sblackwell
03/27/2020
Mathematics
Middle School
Javier worked the following hours in the month of October. What was the percent increase from week 2 to week 4?
Answer:
32%
Step-by-step explanation:
I don’t know. I’m on a test got the answer wrong and it showed me the right answer.
Answer:
56:42 (i hope this is right)
Step-by-step explanation:
I divided 56 and 4 which makes 14. Then I multiplied 14 and 3 to get 42. So 56 by 42.
Answer:
80 machines
Step-by-step explanation:
If a machine makes 20 gadgets every fourth (1/4) of an hour, it makes 80 machines every hour (20*4).
