Answer:
Step-by-step explanation:
Hi there!
We're given that there are 8 marbles in total. 2 marbles are yellow and 3 are red, making the number of red AND yellow marbles 5 (2+3=5)
Because 5 out of the 8 marbles are yellow or red, the probability of choosing one of them is .
I hope this helps!
Answer:
1
Step-by-step explanation:
Hello!
Plug in 2 for x and simplify.
<h3>Evaluate</h3>We could have also simplified the fraction first. If a fraction has the same number in the numerator and the denominator, then it is always equal to 1, no matter what values of x.
The radius of convergence R is 1 and the interval of convergence is (-3, -1) 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 =
and
=
Now limit is taken,
=
=
=
=
= < 1
- 1 < < 1
- 1 - 2 < x < 1 - 2
- 3 < x < - 1
We get that,
interval of convergence = (-3, -1)
radius of convergence R = 1
Hence the radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series.
Learn more about radius of convergence here:
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