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# Series query. watch

1. (Original post by RichE)
Do you use your holidays to post unwelcome pointless dribble?

Try making a constructive comment occasionally. There's a reason for that red gem in the corner of your posts.
hehe...got any better suggestions?
2. (Original post by Phil23)
hehe...got any better suggestions?
none that I could post without getting banned
3. (Original post by RichE)
none that I could post without getting banned
try PM'in them , lol... dont think u can get banned for that
4. Yes that's essentially what I did with the root 2 case. That would extend generally - I just used root 2 to help demonstrate a specific example.

If you wished the limit to be L (any real number) you could use the same idea of dipping into the positives or negatives depending on whether the partial sum was currently below or above L.

Riemann showed (it's not actually that difficult) that any L can be attained from rearranging any series that is convergent but not absolutely convergent.

For an absolutely convergent series the positives will add to some finite limit and similarly the negatives. So it isn't possible to keep dipping into an infinite sum of positives or negatives as we had earlier. In the AC case even taking all the posl at once the effect would be finite.
Thanks for that. I'm just moving onto absolute convergence but will bear in mind the distinction between convergent and absolutely convergent.

(Original post by Phil23)
do you use your holidays what they are used for ...sleeping..resting....sleeping some more?!?!?

STOP STUDYING, lol
Well my part time job is very very boring and pointless so I need this to compensate and thus add some form of purpose to this summer. Besides, I can spare an hour or two a day for something i'm interested in.
5. (Original post by Gaz031)
Well my part time job is very very boring and pointless so I need this to compensate and thus add some form of purpose to this summer. Besides, I can spare an hour or two a day for something i'm interested in.
that reminds me i have to get down to some work one of these days..got so much uni prep work to do, lol...two fat booklets of problem sheets...

...btw...anyone knwo what "verify" means? A question asked me to verify some series expansions? how do i do that? plug in values and show LHS~RHS or derive the series from scratch?

cheers

pk
6. (Original post by Phil23)
...btw...anyone knwo what "verify" means? A question asked me to verify some series expansions? how do i do that? plug in values and show LHS~RHS or derive the series from scratch?
"Verify" means "show to be true"

Don't you have a dictionary?
7. (Original post by RichE)
"Verify" means "show to be true"

Don't you have a dictionary?
i do, but what does it mean in this context - its on problem sheet 5 if you have your stuff from last summer

cheers

pk
8. (Original post by Phil23)
i do, but what does it mean in this context - its on problem sheet 5 if you have your stuff from last summer

cheers

pk
Well, it's gonna mean the same as "show" or "prove".

So how would you prove that e^x equals the given power series? Why not try calculating the Taylor coefficients

f(n)(0)/n!

of f(x) = e^x centred at 0.
9. Its ok RichE - I for one think TSR should begin exercising a firmer policy on kiddie sign up. Personally, I wouldn't let kiddies get on the internet at all, lest they run into guys like those over in the Health forum and they start filling their minds with such boredom they become even more inclined to be suicidal.
10. (Original post by Phil23)
i do, but what does it mean in this context - its on problem sheet 5 if you have your stuff from last summer

cheers

pk
His "stuff from last year" isn't the "stuff" you're having troubles with now.

Instead of being rude I suggest you should show some respect!
11. (Original post by Galois)
His "stuff from last year" isn't the "stuff" you're having troubles with now.

Instead of being rude I suggest you should show some respect!
Don't worry yourself, Galois
12. (Original post by Phil23)
do you use your holidays what they are used for ...sleeping..resting....sleeping some more?!?!?

STOP STUDYING, lol
**** holiday you're having then, Maths is interesting and way better than sleeping endlessly that's for sure.

And on results day Gaz is coming to Creation with me and the crew so don't knock him!
13. (Original post by Nima)
**** holiday you're having then, Maths is interesting and way better than sleeping endlessly that's for sure.

And on results day Gaz is coming to Creation with me and the crew so don't knock him!
why would i knowck him...he's a friend - what does that even mean, lol, and what is creation..a film?
14. (Original post by RichE)
Well, it's gonna mean the same as "show" or "prove".

So how would you prove that e^x equals the given power series? Why not try calculating the Taylor coefficients

f(n)(0)/n!

of f(x) = e^x centred at 0.
hmmm...still at a loss as to how that would 'verify' the validity of the series
15. (Original post by Phil23)
hmmm...still at a loss as to how that would 'verify' the validity of the series
What do you mean? First of all you can prove that f(x) = SUM f(n)(0)/n! [n = 0 to infinity]

and then you can apply this to f(x) = ex

this is enough to verify that f(x) is equal to the series stated.
16. (Original post by Phil23)
hmmm...still at a loss as to how that would 'verify' the validity of the series
Determine the Taylor series - I doubt you're expected to deal with convergence issues at this stage.
17. And on results day Gaz is coming to Creation with me and the crew so don't knock him!
I am? Do I get any say in this?
18. (Original post by Gaz031)
I am? Do I get any say in this?
are these two friends you didn't know you had, Gaz?
19. (Original post by RichE)
are these two friends you didn't know you had, Gaz?
Naaah we live near each other and he is actually coming on results day. Phil on the other hand...need I say more :|
20. (Original post by Nima)
Phil on the other hand...need I say more :|
Well maybe I'm being too hard on Phil. Maybe I shouldn't lecture him until he's in Oxford

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