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 ∞ ( − 1 ) n + 1 3.7.11 ⋯ ( 4 n − 1 ) ( x − 1 ) n 4 n
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 ∞ ( − 1 ) n + 1 3.7.11 ⋯ ( 4 n − 1 ) ( x − 1 ) n 4 n
Solution Summary: The author calculates the Interval of convergence of the power series.
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
∞
(
−
1
)
n
+
1
3.7.11
⋯
(
4
n
−
1
)
(
x
−
1
)
n
4
n
Using the Alternating Series Test determine whether the series diverges or converges, if possible evaluate the series.
Proof In Exercises 17–20, prove that the Maclaurin series for the function converges to the function for all x.
Study the power series:
- Using Limit Comparison Test show that this series converges when x = −2.
- Justify if the series is absolutely convergent, conditionally convergent, or divergent at x = 12?
- Determine the radius and interval of convergence of the power series.
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