# Tagged Questions

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### Finding the convergence

The sequence $a_n = \sqrt[n]{(3^n+5^n)}$ is convergent? Tried to resolve applying the the limit $n\to\infty$ but couldn't figure out how to finish it, any idea? Thanks
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### Why does $\sum_{k=1}^{\infty} \frac {(-1)^{k-1}}{k}$ converge conditionally?

Why does it converge conditionally? $$\sum_{k=1}^{\infty} \frac {(-1)^{k-1}}{k}$$
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### How to apply the alternating series test to the series $\sum (-1)^{n+1} n/2^n$?

So, I need to test the following series for convergence or divergence: $$\sum_{n=1}^\infty (-1)^{n+1}{n\over {2^n}}$$ I know that when you use the Alternating Series Test, the series must satisfy ...
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### Is the following series converging or diverging. $\sum_{n=1}^{\infty}\dfrac{n+4^n}{n+6^n}$

I know one solution. That is by Doing comparison with $\dfrac{4^n+4^n}{6^n}$ Wondering if there are more ways to do it
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### Problem with proof that positive infinite series are commuative

Proof from real analysis book: Let $\sum_{n=0}^{\infty}a_n$ converge, where $a_n \geq 0, n \in \mathbb{N}$. Then the series $$\sum_{k=1}^{\infty}a'_k = a'_1 + a'_2 + \cdots + a'_k + \cdots$$ ...
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### Convergence of $a_n=1+1/5+1/9+\ldots+\frac{1}{4n-3}$

Show that the sequence $$a_n=1+1/5+1/9+\ldots+\frac{1}{4n-3}$$ does not converge but the sequence $b_n=\frac{a_n}{n}$ converges. I can show the first part. For the second part, will it be sufficient ...
This seems to be physics question, but the problem just concerns math. Preface If one wants to calculate the permeance $P$ of a rectangular bar: it is an easy task: $$P = \frac{\mu a b}{L} ... 1answer 35 views ### Simpler way of proving series convergence? Determine whether the following series converges$$\sum_{n=1}^{\infty} \left (\frac{n^4}{n^4 + 2}\right)^{n^5-3}.$$I've found convergence using the root criterion in the following way. \sqrt[n]{ ... 3answers 68 views ### A sequence and convergence Let \{x_n\} and \{y_n\} be sequences of real numbers which converge to \ell and m respectively. Show that$$\lim_{n\to \infty} \frac{1}{n}\sum_{k=1}^{n}x_ky_{n+1-k}=\ell m This is a ...
This question is inspired by this question: Solutions for $\frac{dy}{dx}=y$?. It makes me wonder if there are any function where the sum of all antiderivative and derivative converges. The ...