I need help figuring out what process to use to complete this problem. If p, q, and r are all positive then what is the collection of all positive values p, q, and r that cause all three series in the picture to converge?p>0, q>0, r>1p>1, q>1, r>0p>1, q>1, r>1p>1, q>0, r>0 The image presents three infinite series:1. $\sum_{n=1}^{\infty} \frac{1}{n^p}$2. $\sum_{n=1}^{\infty} \frac{1}{q^n}$3. $\sum_{n=1}^{\infty} \frac{(-1)^n}{n^r}$The first series is a p-series, where $p$ is a constant. The second series is a geometric series with the term $\frac{1}{q^n}$, where $q$ is a constant. The third series is an alternating series, indicated by $(-1)^n$, divided by $n^r$, where $r$ is a constant.

The objective here is to find the condition on p, q, and r for which the given series will be…

Answered: I need help figuring out what process…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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I need help figuring out what process to use to complete this problem. If p, q, and r are all positive then what is the collection of all positive values p, q, and r that cause all three series in the picture to converge?

p>0, q>0, r>1
p>1, q>1, r>0
p>1, q>1, r>1
p>1, q>0, r>0

The image presents three infinite series:

1. $\sum_{n=1}^{\infty} \frac{1}{n^p}$
2. $\sum_{n=1}^{\infty} \frac{1}{q^n}$
3. $\sum_{n=1}^{\infty} \frac{(-1)^n}{n^r}$

The first series is a p-series, where $p$ is a constant. The second series is a geometric series with the term $\frac{1}{q^n}$, where $q$ is a constant. The third series is an alternating series, indicated by $(-1)^n$, divided by $n^r$, where $r$ is a constant.

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