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Assume thatconverges to p =What can YOu say about the convergence of the given series?n8441lim n *0(Enter 'inf' for 0.)En*an OA. convergent B. divergent C...

Question

Assume thatconverges to p =What can YOu say about the convergence of the given series?n8441lim n *0(Enter 'inf' for 0.)En*an OA. convergent B. divergent C. The Ratio Test is inconclusive

Assume that converges to p = What can YOu say about the convergence of the given series? n8441 lim n *0 (Enter 'inf' for 0.) En*an OA. convergent B. divergent C. The Ratio Test is inconclusive



Answers

Determine all values of $p$ for which the series converges. $$\sum_{k=0}^{\infty} \frac{1}{(a+b k)^{p}}, a>0, b>0$$

We want to determine whether or not the given p series converges or diverges. The P series in question is the sum from n equals one to infinity of one over end raised to the power of E. To answer this question, let's relate the most important facts about P series that we thoroughly understand how to salt. Remember that a P series is always in the form of some of one over end raised to the power of P. So the P series converges. It's not only if P the exponent in the denominator is greater than one in this particular problem are some is already of the form over the form one over end of the P where P is equal to eat. Remember that E is equal to two followed by some decimal numbers. So we can conclude for this series that P equals E. Must be greater than one. So that means that the series given by the sum and equals one to infinity of one over N. Raised to the power has to converge.

All right. We want to determine whether or not a given piece series converges or whether it diverges. P series in question is the sum from N equals one to infinity and raised to the negative 0.98 power. Let's remember some important facts about P series. Before we proceed to evaluate the convergence of this given one. So remember that the P series is always in the form some one over end to the P. With that piece series will converge if and only if P the exponent in the denominator is greater than one. We see that our series is not quite the right form to evaluate as a P. Series. But with a simple manipulation, we can answer this problem. So and the negative 10.98 is the same as one of the end of the 10.98 So we can rewrite our series as a sum from N equals one to infinity of one of the end of the 10.98 Which is now in the correct form, P equals 0.98 is less than one, which means that given the criteria are listed here, we must have that the sum from N equals one to infinity at the end of the negative 10.98 diverges.

We want to determine whether or not the given P series converges. The series in question is the sum from N equals one to infinity and raised to the negative pi. Power to evaluate the convergence of the series. Let's relate important facts about P series that allow us to solve the problem. So first and foremost remember that a P series is always a series of the form, some of one over end of the P the p series converges if and only if P the exponent the denominator is greater than one, so end to the negative pi is not quite in the correct form to evaluate this series convergence, but we can rewrite our series in order to evaluate more easily. So and to the negative pi is the same as one over end of the pie. So this series is sum from N equals one to infinity of one over N pi. Now we have the correct form where P is equal to pi, which is definitely greater than one. So we must have the sum from N equals one to infinity of end of the negative pi converges

In this question will be called up from the base. Siri's. We have a formula under submission under one on the end, probably from one up to infinity. And then this is here. It will be convergent if there be created. And one, It would be divergent if there be smaller, equal to one their phone. But a We're given the summation on the one in power three about three and find of cables from one up to infinity. Definite doesn't implies that the p e coach victory and scripture than one therefore miseries there will be convergent in a but B We're given the summation off, the one almost covering okay from one after infinity, not the status. When you can write down into the one, I'm OK about 1/2 and therefore the be equal to 1/2 its minor than one that forget it would be diversion in apostasy were given the submission off the K bomb on this one from one job to infinity and you can read this note your one of a guy one It means done. The be equal to one and one equals to one means done. It will be divergence. Well, in the but city were given the submission off the cape. Our off minus 2/3 vision means no one can understand. Judah One over. Okay, about two out of three. And this understanding B sico Jidda to over three. This manner than one. That organism will be divergent.


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