Question

17. Find the radius of convergence of the following power series.\\ $\sum_{n=1}^{\infty} \frac{(3x - 4)^n}{\ln n}$ \\ (a) 3 (b) 1 (c) $\frac{3}{4}$ (d) $\frac{1}{3}$ (e) 4

          17. Find the radius of convergence of the following power series.\\
$\sum_{n=1}^{\infty} \frac{(3x - 4)^n}{\ln n}$ \\
(a) 3 (b) 1 (c) $\frac{3}{4}$ (d) $\frac{1}{3}$ (e) 4

17. Find the radius of convergence of the following power series.

∑n=1^∞((3x - 4)^n)/(ln n)

(a) 3 (b) 1 (c) (3)/(4) (d) (1)/(3) (e) 4

Added by Amber J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sam Stansfield

05/11/2023

Step 1

The ratio test states that for a power series \sum a_nx^n, the radius of convergence R is given by: R = lim (n->∞) |a_(n+1)/a_n| In this case, a_n = (3x-4)^n/ln(n). Show more…

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Find the radius of convergence of the following power series. sum_(n=1)^(infty ) ((3x-4)^(n))/(lnn) (a) 3 (b) 1 (c) (3)/(4) (d) (1)/(3) (e) 4 17. Find the radius of convergence of the following power series 3x-4)r 1n n n=1 (a) 3 (b) 1 (c) 31 I (d) 1I3 (e) 4