Answer:
The series is absolutely convergent.
Step-by-step explanation:
By ratio test, we find the limit as n approaches infinity of
|[a_(n+1)]/a_n|
a_n = (-1)^(n - 1).(3^n)/(2^n.n^3)
a_(n+1) = (-1)^n.3^(n+1)/(2^(n+1).(n+1)^3)
[a_(n+1)]/a_n = [(-1)^n.3^(n+1)/(2^(n+1).(n+1)^3)] × [(2^n.n^3)/(-1)^(n - 1).(3^n)]
= |-3n³/2(n+1)³|
= 3n³/2(n+1)³
= (3/2)[1/(1 + 1/n)³]
Now, we take the limit of (3/2)[1/(1 + 1/n)³] as n approaches infinity
= (3/2)limit of [1/(1 + 1/n)³] as n approaches infinity
= 3/2 × 1
= 3/2
The series is therefore, absolutely convergent, and the limit is 3/2
Answer:
12500
Step-by-step explanation:
$2 are received for 1000 hits
So, $1 received for 1000/2 = 500 hits
Number of hits required to make $25
= 25*500
=12500
The length of the windshield wiper to the nearest inch is 24 inches
<h3>How to calculate the area of a sector</h3>
The formula for calculating the area of a sector is given as:
A = r²β/2
r is the length of the wiper
β is the subtended angle
Given the following
A = 500.3 square in
β = 98 degrees = 98pi/180 = 49pi/90
Substitute
500.3 = r²49pi/180
500.3 = 153.86r²/180
153.86r² = 90054
r² = 585.298
r = 24.19
Hence the length of the windshield wiper to the nearest inch is 24 inches
learn more on sector here: brainly.com/question/22972014
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6 < c < 20,
Of course if you knew the triangle was a right triangle you could use the Pythagorean theorem to directly get the size of the third side.
By evaluating the <em>linear</em> function f(x) = x - 3 at x = 5 and discarding the another function in the table given, we conclude that f(5) = 2 belongs to that <em>linear</em> equation.
<h3>What function contains a given relationship?</h3>
In this problem we must check if the given relationship between the <em>independent</em> variable (x) and the <em>dependent</em> variable (y) exists in any of the two functions: (i) a table, (ii) an expression.
After a quick analysis, we conclude that f(5) = 2 is a point of the linear function f(x) = x - 3. Here is the proof:
f(5) = 5 - 3
f(5) = 2
To learn more on linear equations: brainly.com/question/11897796
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