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 n ! ( x − 5 ) n 3 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 n ! ( x − 5 ) n 3 n
Solution Summary: The author explains how the power series diverges for left|x-5right|mathrm>0 by ratio test and converges only at the point
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.)
Using the root test, the series E(-1)"(1-2)
n2
(A) The root test fails.
(B) Converges conditionally
(C) Diverges
(D) Converges absolutely
(E) None of the above.
A O
B O
.C
D O
E O
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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