Answer:
(a) Initial ticket = 60
(b) 5 tickets
Step-by-step explanation:
Given
Solving (a): Initial Tickets
A linear function is represented as:
Where c is the initial value
In this case, c represents the initial tickets.
By comparing
to
Solving (b): Tickets needed on each ride
This represents the rate
In , m represents the rate
By comparing
to
It is negative because 5 tickets is subtracted for each ride.
Hence, the number of ticket per ride is 5
The radius of convergence R is ∞ and the interval of convergence is (-∞, ∞) for the given power series. This can be obtained by using ratio test.
<h3>Find the radius of convergence R and the interval of convergence:</h3>Ratio test is the test that is used to find the convergence of the given power series.
First aₙ is noted and then aₙ₊₁ is noted.
For ∑ aₙ, aₙ and aₙ₊₁ is noted.
= β
Here aₙ = (n²/n!) xⁿ⁺³ and aₙ₊₁ = ((n+1)²/(n+1)!) xⁿ⁺¹⁺³ = ((n+1)²/(n+1)!) xⁿ⁺⁴
Now limit is taken,
=
=
=
= = 0 < 1
Since the limit is less than 1 the series is converging.
We get that,
interval of convergence = (-∞, ∞)
radius of convergence R = ∞
Hence the radius of convergence R is ∞ and the interval of convergence is (-∞, ∞) for the given power series.
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