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KonradZuse
 3 years ago
Alternating series Q:
KonradZuse
 3 years ago
Alternating series Q:

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KonradZuse
 3 years ago
Best ResponseYou've already chosen the best response.0In the book there is an example that's \[\sum_{n=1}^{\infty} \frac{n}{(2)^{n1}}\]

vf321
 3 years ago
Best ResponseYou've already chosen the best response.1Well if n>infinity, then n/(n+1) is 1 since n goes to infinity at the same rate. We also know that the base case, n = 1, IS 1/2, and that the function's monotonic, so n/(n+1) HAS to be between 1/2 and 1...

vf321
 3 years ago
Best ResponseYou've already chosen the best response.1Slight note: Monotonic over [1, infty]

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0how or why? the how is clear right? if \(n>1\) then \(\frac{n+1}{n}>\frac{1}{2}\) for sure

vf321
 3 years ago
Best ResponseYou've already chosen the best response.1Well that's a property of your book's proof. If you like, we can probably do an ALTERNATE one (get it?).

vf321
 3 years ago
Best ResponseYou've already chosen the best response.1NVM. The point is, whatever your book is doing to prove the alternating series converges, it needs that fact...

vf321
 3 years ago
Best ResponseYou've already chosen the best response.1Well do you have to make a formal proof? Or an AP Calc BCsuitable proof?

KonradZuse
 3 years ago
Best ResponseYou've already chosen the best response.0Do we have to do stuff like this, or just apply the rules in the theorm to see if it wortks or not?

vf321
 3 years ago
Best ResponseYou've already chosen the best response.1lol it was ap calc bc. Nice guess on my part, huh? Yeah for AP you just say "this converges by ALT series test" because of the three conditions for alternating series. Do you know them?

KonradZuse
 3 years ago
Best ResponseYou've already chosen the best response.0The course I'm in is Calc 2.

KonradZuse
 3 years ago
Best ResponseYou've already chosen the best response.0The book only says 2 conditons an+1 < an and an = 0.

KonradZuse
 3 years ago
Best ResponseYou've already chosen the best response.0I did the question I was goign to do and was correct, but I did do it a diff way than the professor..

vf321
 3 years ago
Best ResponseYou've already chosen the best response.1Well in that case I can't guess your course needs... and the third condition is that the "non alternating part" has to be always positive.

KonradZuse
 3 years ago
Best ResponseYou've already chosen the best response.0Seems like a lot of L'hospitals rule is used.. Should bone up.

KonradZuse
 3 years ago
Best ResponseYou've already chosen the best response.0oh yeah it says let an > 0

vf321
 3 years ago
Best ResponseYou've already chosen the best response.1LH is a good thing to always keep in your mind.

KonradZuse
 3 years ago
Best ResponseYou've already chosen the best response.0so hmm... can you check out the first picture and see what they are doing?

KonradZuse
 3 years ago
Best ResponseYou've already chosen the best response.0not sure if it's important for my needs.
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