(a) Sincelimk+(x 4)k+1/k + 1(x 4)k/k= limk+ kk + 1(x 4)=
Chapter 9, Problem 4(choose chapter or problem)
(a) Since
\(\lim _{k \rightarrow+\infty}\left|\frac{(x-4)^{k+1} / \sqrt{k+1}}{(x-4)^{k} / \sqrt{k}}\right|=\lim _{k \rightarrow+\infty}\left|\sqrt{\frac{k}{k+1}}(x-4)\right|\)
\(=|x-4|\)
he radius of convergence for the infinite series \(\sum_{k=1}^{\infty}(1 / \sqrt{k})(x-4)^{k}\) is _______.
(b) When \(x=3\),
\(\sum_{k=1}^{\infty} \frac{1}{\sqrt{k}}(x-4)^{k}=\sum_{k=1}^{\infty} \frac{1}{\sqrt{k}}(-1)^{k}\)
Does this series converge or diverge?
Equation Transcription:
Text Transcription:
lim _k right arrow + infinity |(x-4)^k+1/ sqrt k+1 /(x-4)^k/ sqrt k| = lim_k right arrow + infinity |k/k+1(x-4) =|x-4|
sum_k=1^ infinity (1/ sqrt k)(x-4)^k
x=3
sum_k=1^infinity 1/sqrt k (x-4)^k = sum_k=1^ infinity 1/sqrt k (-1)^k
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer