Question

Find the interval of convergence for the power series ?_{n=0}^{?} rac{(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) Converges only at x = 3 c) [-5, 11] d) (-?, ?) e) (-5, 11]

          Find the interval of convergence for the power series ?_{n=0}^{?} rac{(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) Converges only at x = 3
c) [-5, 11]
d) (-?, ?)
e) (-5, 11]

Find the interval of convergence for the power series ?n=0^? rac(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) Converges only at x = 3
c) [-5, 11]
d) (-?, ?)
e) (-5, 11]

Added by Monica B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Tim Thornhill

Step 1

We can use the ratio test: lim |(n+1)8x^(n+1)/(n8x^n)| = lim |8x| = 8|x| This limit exists for all x, so the series converges for all x within a radius of convergence of R=1/8. Show more…

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Find the interval of convergence for the power series ∑_{n=0}^∑ ∞ (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) Converges only at x = 3 c) [-5, 11] d) (-∞, ∞) e) (-5, 11]