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
1,325-35=1,290
50x25=1,250 50x26=1,300
25 months
Sum of a finite geometric series=a(r^(n) -1)/(r -1)
or
sum of a finite geometric series=a(1 - r^(n))/(1 - r)
the Smiths would spend a total of $2928.2 on clothing in 4 years
Answer:
60-9pi if you need that rounded then 31.73
Step-by-step explanation:
10*6= 60
the two semi circles make one full circle. a circle formula is pi*r^2 = pi*3^2= 9pi
then subtract 9pi from 60
60-9pi = 31.73
Answer:
3 hundredths or .03
Step-by-step explanation:
