Hi, all. I need to evaluate the following: where k∈ℕ and k≠1 I don't really know how to do much else than test whether or not a series converges or diverges; I don't know how to determine what it converges to. Thanks, guys!
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Originally Posted by hatsoff Hi, all. I need to evaluate the following: where k∈ℕ and k≠1 I don't really know how to do much else than test whether or not a series converges or diverges; I don't know how to determine what it converges to. Thanks, guys! I will give you a hint Rewrite as Now consider that since that Get it now?
Originally Posted by Mathstud28 I will give you a hint Rewrite as Now consider that since that Get it now? It resembles a geometric series in that respect, but then each term is multiplied by n, which is not a constant. I don't know how to handle that.
Originally Posted by hatsoff It resembles a geometric series in that respect, but then each term is multiplied by n, which is not a constant. I don't know how to handle that. Think derivative/integration
Originally Posted by Mathstud28 Think derivative/integration I need another hint, sir.
Originally Posted by hatsoff Hi, all. I need to evaluate the following: where k∈ℕ and k≠1 I don't really know how to do much else than test whether or not a series converges or diverges; I don't know how to determine what it converges to. Thanks, guys! If , Now let , since , we have and . So we can apply the infinte Geometric Progression formula
Originally Posted by hatsoff I need another hint, sir. Oh I am sorry! I completely missed your response. Luckily for you The oh so competent Isomorphism replied
Originally Posted by Mathstud28 Think derivative/integration Hmm. Are you telling me that the following is true: ? If so, then: EDIT: I guess I'm late to the party.
Originally Posted by hatsoff Hmm. Are you telling me that the following is true: ? If so, then: EDIT: I guess I'm late to the party. Yes you are...but for your sake yes..In a power series The same applies for derivatives to prove it expand...differentiate/integrate....contract into an explicit form power series and compare
Originally Posted by Mathstud28 Yes you are...but for your sake yes..In a power series The same applies for derivatives to prove it expand...differentiate/integrate....contract into an explicit form power series and compare The following phrase should be added to this: "Provided the relevant series converge." If they don't then these rules go out the window. -Dan
Originally Posted by topsquark The following phrase should be added to this: "Provided the relevant series converge." If they don't then these rules go out the window. -Dan Yes! Thank you! Sometimes I have the classic "I already know it so I assume others do to" syndrome...not a good thing to have
Thanks, guys! This was a big help.
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