<u>Given</u>:
Given that the measure of ∠CDR = 85°
We need to determine the measure of and
<u>Measure of arc RC:</u>
Since, we know that if a central angle is formed by two radii of the circle then the central angle is equal to the intercepted arc.
Thus, we have;
Substituting the values, we get;
Thus, the measure of is 85°
<u>Measure of arc CBR:</u>
We know that 360° forms a full circle and to determine the measure of arc CBR, let us subtract the values 360 and 85.
Thus, we have;
Substituting the values, we have;
Thus, the measure of is 275°
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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