Solved: 14 Select between converges or diverges to fill the first blank.Sincelimk+(k +

Chapter 9, Problem 3

(choose chapter or problem)

Select between converges or diverges to fill the first blank.

Since

                                \(\lim _{k \rightarrow+\infty} \frac{(k+1) ! / 3^{k+1}}{k ! / 3^{k}}=\lim _{k \rightarrow+\infty} \frac{k+1}{3}=+\infty\)

the series \(\sum_{k=1}^{\infty} k ! / 3^{k}\) ________ by the ________ test.

Equation Transcription:

_____

Text Transcription:

lim over k rightarrow +infty (k+1)!/3^k+1/k!/3^k= lim over k rightarrow +infty k+1/3=+infty

sum _k=1 ^infty k!/3^k_____

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