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

vf321 Group TitleBest ResponseYou've already chosen the best response.1
Well 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...
 2 years ago

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

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

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

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

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

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

vf321 Group TitleBest ResponseYou've already chosen the best response.1
lol 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?
 2 years ago

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

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

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

vf321 Group TitleBest ResponseYou've already chosen the best response.1
Well 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.
 2 years ago

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

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

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

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

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