Help with determining if a series is convergent or divergent question (1 Viewer)

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1. The problem statement, all variables and given/known data

Problem is attached in this post.

2. Relevant equations

Problem is attached in this post.

3. The attempt at a solution

I know how to find the sum of this series, but I don't know what method to use in order to prove that this series converges. Also I don't understand how I'm supposed to tell as to whether or not this is a geometric series.
 

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Dick

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1. The problem statement, all variables and given/known data

Problem is attached in this post.

2. Relevant equations

Problem is attached in this post.

3. The attempt at a solution

I know how to find the sum of this series, but I don't know what method to use in order to prove that this series converges. Also I don't understand how I'm supposed to tell as to whether or not this is a geometric series.
It's not geometric because the ratio of consecutive terms isn't a constant, but that ratio does approach a limit. Is that enough of a clue?
 
It's not geometric because the ratio of consecutive terms isn't a constant, but that ratio does approach a limit. Is that enough of a clue?
Would the limit have to be 0 for the series to convergent?

Lim (3^n + 4^n)/(7^n) n -> ∞ = 0 For the series to be convergent? (I actually tried this, but can't seem to find a method to solve for such a limit).
 
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Dick

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Would the limit have to be 0 for the series to convergent?

Lim (3^x + 4^x)/(7^x) n -> ∞ = 0 For the series to be convergent? (I actually tried this, but can't seem to find a method to solve for such a limit).
You mean Lim (3^n + 4^n)/(7^n) n -> ∞ = 0. You should be able to. Divide numerator and denominator by 7^n. But that's not what I'm talking about. I'm talking about the ratio ##\frac{a_{n+1}}{a_n}##.
 

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