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

vf321Best 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...
 one year ago

vf321Best ResponseYou've already chosen the best response.1
Slight note: Monotonic over [1, infty]
 one year ago

satellite73Best 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
 one year ago

vf321Best 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?).
 one year ago

vf321Best 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...
 one year ago

vf321Best ResponseYou've already chosen the best response.1
Well do you have to make a formal proof? Or an AP Calc BCsuitable proof?
 one year ago

KonradZuseBest 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?
 one year ago

vf321Best 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?
 one year ago

KonradZuseBest ResponseYou've already chosen the best response.0
The course I'm in is Calc 2.
 one year ago

KonradZuseBest ResponseYou've already chosen the best response.0
The book only says 2 conditons an+1 < an and an = 0.
 one year ago

KonradZuseBest 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..
 one year ago

vf321Best 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.
 one year ago

KonradZuseBest ResponseYou've already chosen the best response.0
Seems like a lot of L'hospitals rule is used.. Should bone up.
 one year ago

KonradZuseBest ResponseYou've already chosen the best response.0
oh yeah it says let an > 0
 one year ago

vf321Best ResponseYou've already chosen the best response.1
LH is a good thing to always keep in your mind.
 one year ago

KonradZuseBest ResponseYou've already chosen the best response.0
so hmm... can you check out the first picture and see what they are doing?
 one year ago

KonradZuseBest ResponseYou've already chosen the best response.0
not sure if it's important for my needs.
 one year ago
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