Sincelimk+(3k+1xk+1)/(k + 1)!(3kxk)/k! = limk+3xk + 1 = 0the interval of convergence for
Chapter 9, Problem 3(choose chapter or problem)
Since
\(\lim _{k \rightarrow+\infty}\left|\frac{\left(3^{k+1} x^{k+1}\right) /(k+1) !}{\left(3^{k} x^{k}\right) / k !}\right|=\lim _{k \rightarrow+\infty}\left|\frac{3 x}{k+1}\right|=0\)
the interval of convergence for the series \(\sum_{k=0}^{\infty}\left(3^{k} / k !\right) x^{k}\) is ______.
Equation Transcription:
Text Transcription:
Lim_k right arrow + infinity |(3^k+1 x^k+1)/(k+1)!/ (3^kx^k)/k!| = lim _k right arrow + infinity |3x/k+1|=0
sum_k=0^ infinity (3^k/k!)x^k
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