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

Chapter 9, Problem 2

(choose chapter or problem)

Select between converges or diverges to fill the first blank.

Since

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

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

Equation Transcription:

_____

Text Transcription:

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

sum_k=1 ^infty k^3/3^k_____

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