Finding the Interval of Convergence In Exercises 15-38, find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.) ∑ n − 1 ∞ 2.3.6 ⋯ 2 n 3.5.7 ⋯ ( 2 n + 1 ) x 2 n + 1
Finding the Interval of Convergence In Exercises 15-38, find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.) ∑ n − 1 ∞ 2.3.6 ⋯ 2 n 3.5.7 ⋯ ( 2 n + 1 ) x 2 n + 1
Solution Summary: The author explains that the interval of convergence is [-1, 1].
Finding the Interval of Convergence In Exercises 15-38, find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.)
∑
n
−
1
∞
2.3.6
⋯
2
n
3.5.7
⋯
(
2
n
+
1
)
x
2
n
+
1
Calculus 2 Question:
Follow up to my previous question:
Test the endpoints of the interval for convergence using the Alternating Series Test or the p-series test. Show your work, and justify your answer.
Interval of Convergenece: -1/2<x<1/2
power series: using the Ratio Test or the Root Test to determine the radius of convergence, and indicate the open interval of convergence.
(a) Find the series' radius and interval of convergence. Find the values of x for which the series converges (b) absolutely and (c) conditionally.
nx"
n=0 11"
(a) The radius of convergence is.
(Simplify your answer.)
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