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
- If β < 1, then the series converges
- If β > 1, then the series diverges
- If β = 1, then the series inconclusive
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.
Learn more about power series here:
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Answer:
The percent of the people who prefer fresh fruit is 61.9%
Step-by-step explanation:
Assume x% people prefer fresh fruit over canned fruit. Then x can be calculated as:
x= <u>No of people who prefer fresh fruit </u> * 100
Total no of surveyed people
x =<u> 13 </u> * 100
21
x = 61.9%
Answer:
Step-by-step explanation:
We know that the height of a parallelogram can be found by divind the area by the lenght of the base.
The area is 4x2 – 2x + 5 and the base is 2x – 6. To find the height, we need to divide both polynomials:
9514 1404 393
Answer:
a) $3.45
b) P(x) = 0.0003x -18
c) $3.00, A
Step-by-step explanation:
a) When the family income is $71,500, it exceeds $70,000 by ...
$71,500 -70,000 = $1500
Then the price of the child's lunch will be ...
$3.00 + 0.0003×1500 = $3.45
__
b) For family income in the given range, the price of a lunch will be ...
P(x) = 3.00 + 0.0003(x -70000) = 3.00 +0.0003x -21.00
P(x) = 0.0003x -18.00
__
c) P(70000) = 0.0003×70000 -18 = 3×7-18 = 3.00
The definition of P(x) in part (b) tells you the meaning of this. x=70,000 is the family's annual income; P(x) is the price of a lunch.
P(70,000) is the price of a lunch for a child whose family annual income is $70,000.
Answer:
I got you it
Step-by-step explanation:
B and have a good day
