Find if the sequence converges or diverges. If the sequence converges find its limit.P.S.- Given that I wrote out the sequence and found the pattern I know the limit is equal to 8. However, I am not sure how to prove that. In other words I know the answer I just need the steps on how to get there. Just answer as if I didn't know the answer. Thank you. 3. $\left\{ \sqrt[n]{2^{1+3n}} \right\}_{n=0}$This expression represents a sequence where each term is given by the formula inside the braces. The term involves:- $\sqrt[n]{}$: The nth root.- $2^{1+3n}$: An exponential expression with a base of 2 raised to the power of $1 + 3n$.- $n = 0$: The sequence begins at $n = 0$.This formula is used to define the terms of a sequence, where $n$ varies from 0 onwards.

Answered: 3. {V21+3n

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Find if the sequence converges or diverges. If the sequence converges find its limit.

P.S.- Given that I wrote out the sequence and found the pattern I know the limit is equal to 8. However, I am not sure how to prove that. In other words I know the answer I just need the steps on how to get there. Just answer as if I didn't know the answer. Thank you.

3. $\left\{ \sqrt[n]{2^{1+3n}} \right\}_{n=0}$

This expression represents a sequence where each term is given by the formula inside the braces. The term involves:

- $\sqrt[n]{}$: The nth root.
- $2^{1+3n}$: An exponential expression with a base of 2 raised to the power of $1 + 3n$.
- $n = 0$: The sequence begins at $n = 0$.

This formula is used to define the terms of a sequence, where $n$ varies from 0 onwards.

Expert Solution

Step 1

Recall:

$A Sequence is said to be convergent if it approaches some limit . i . e, A sequence < a_{n} > converges to the limit (say) L . \Rightarrow \lim_{n \to \infty} a_{n} = L . If a_{n} does not converge, it is said to diverge .$