Question

Find the interval of convergence for the power series ?_{n=0}^{?} frac{(x-3)^n}{n^5 8^n} Note: This is the same series as the problem asking for the radius of convergence. a) (-5, 11] b) [-5, 11) c) Converges only at x = 3 d) [-5, 11] e) (-?, ?)

          Find the interval of convergence for the power series ?_{n=0}^{?} frac{(x-3)^n}{n^5 8^n}
Note: This is the same series as the problem asking for the radius of convergence.
a) (-5, 11]
b) [-5, 11)
c) Converges only at x = 3
d) [-5, 11]
e) (-?, ?)

$Find the interval of convergence for the power series ?n=0^? frac(x-3)^nn^5 8^n Note: This is the same series as the problem asking for the radius of convergence. a) (-5, 11] b) [-5, 11) c) Converges only at x = 3 d) [-5, 11] e) (-?, ?)$

Added by Rachael H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

07/06/2023

Step 1

Since it is not given, let's assume the general term is: $$a_n(x) = c_n(x-3)^n$$ Now, we need to find the interval of convergence using the Ratio Test. The Ratio Test states that if: $$\lim_{n \to \infty} \left|\frac{a_{n+1}(x)}{a_n(x)}\right| < 1$$ then the Show more…

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Find the interval of convergence for the power series (r_3)" n & Note: This is the same series as the problem asking for the radius of convergence a) (-5,11] b) [-5,11) c) Converges only at x = 3 d) [-5,11] e) (-o)