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Math Question
| Good [+1]Toggle ReplyLink» neoform replied on Mon Jan 23, 2006 @ 2:55pm |
 Coolness: 339715 | Man, I'm so glad I never have to take calculus.. who cares if it converges of diverges?! When am I ever going to use this stuff..? I'm not a freakin physist! |
| Good [+1]Toggle ReplyLink» basdini replied on Mon Jan 23, 2006 @ 2:56pm |
 Coolness: 145250 | |
| Good [+1]Toggle ReplyLink» mdc replied on Mon Jan 23, 2006 @ 9:45pm |
 Coolness: 148865 | haha
that's great so you wanna know what sigma 1/(4^i) converges to? well... in this case, you can take the first 5-6 terms and you'll have a general estimate of what it converges to... because this does indeed converge as i increases, the number you're adding decreases, and eventually is approximated by zero i dont exactly remember how to find the convergence though.. it involves an Sk reduction to partial sums and such... oh god i hated this stuff... and come to think of it.. the Sum of 1/(4^i) seems vaguely similar to the harmonic series.. and may actually diverge.... guh... i cant remember this |
| Good [+1]Toggle ReplyLink» nothingnopenope replied on Mon Jan 23, 2006 @ 10:10pm |
 Coolness: 201275 | Man I'm going to be having nightmares about this for weeks now... I have no idea how I made it through cal |
| Good [+1]Toggle ReplyLink» moondancer replied on Tue Jan 24, 2006 @ 1:26am |
 Coolness: 92315 | Okay well you guys actually helped a lot. Flo, yes I am looking for that point where the curve starts to even out a bit, I still don't get it but I'll have to go with what Dino says about doing the first 5 or 6 calculations for now, and ugh I don't have the patience to think anymore so I'll just have to try and come in early tommorow and ask my teacher and if I get a good answer to find this point of convergence I'll let you guys know cause I'm sure it's bothering one or two people by now. I feel smarter now that I know I'm not alone. Thanks everybody! p.s: This is what happens when you miss class :S, and my class isn't even calculus! |
| Good [+1]Toggle ReplyLink» flo replied on Tue Jan 24, 2006 @ 1:37am |
 Coolness: 146375 | well, i checked more thoroughly and there's no such general formula that gives you the convergence value of an infinite sum. you can calculate its limit (which is finite), and even its integrate.
but yes, if your sum isn't too much complicated and if you've got a little time ahead of you, you can calculate the first iterations of your series until two following values are close enough for you (which is a dirty way to bound the absolute difference under x%, like i mentioned earlier). anyway, good luck for it, and feel free to ask for more in computer science (that's my playing area) or in maths (that's the basis of my playing area even though i'm not as good as i'm supposed to) |
| Good [+1]Toggle ReplyLink» moondancer replied on Tue Jan 24, 2006 @ 2:09am |
| Coolness: 92315 | Well in my excercises there is no specific type of answer we are supposed to arrive at, my instructions are simply "evaluate the sum", but we are expected to understand this for recursive algorithms and calculating running times... or something like that. I think my teacher is just gay! |
| Good [+1]Toggle ReplyLink» Zz.ee.vV replied on Tue Jan 24, 2006 @ 2:18am |
 Coolness: 194075 | the sum seriies of any natural numbers independent of the index will converge at infinity.
sum series that decrease with i will asymptote towards zero, there are equations to dig via the last-sound-point beyond which it becomes too miniscule to count so you just average it. it really depends to which decimal poing of precision you wish to go. if after you apply the formula you use for the series manually you reach 0.0001 after the 10th term, its safe to say you can stop :b |
| Good [+1]Toggle ReplyLink» flo replied on Tue Jan 24, 2006 @ 12:38pm |
| Coolness: 146375 | Originally posted by ZE`EV ...
the sum seriies of any natural numbers independent of the index will converge at infinity. uh ? a sum of anything independant of the index is just a constant, and then the sum operator has no purpose... or didn't i get what you meant ? sum series that decrease with i will asymptote towards zero, [...] not necessarily ; it's very likely that an asymptote can be found, but you can't know before calculating it whether it will be X-parallel, Y-parallel, or a Y=aX+b line. i agree with the remainder, though :) |
| Good [+1]Toggle ReplyLink» nothingnopenope replied on Tue Jan 24, 2006 @ 7:48pm |
| Coolness: 201275 | everyone loves math!
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| Good [+1]Toggle ReplyLink» Zz.ee.vV replied on Tue Jan 24, 2006 @ 9:39pm |
| Coolness: 194075 | Originally posted by FLO...
Originally posted by Ze`ev ...
the sum seriies of any natural numbers independent of the index will converge at infinity. uh ? a sum of anything independant of the index is just a constant, and then the sum operator has no purpose... or didn't i get what you meant ? I meant infinite series as mentioned in the original post... ehhe sorry didnt elaborate enough. sum series that decrease with i will asymptote towards zero, [...] not necessarily ; it's very likely that an asymptote can be found, but you can't know before calculating it whether it will be X-parallel, Y-parallel, or a Y=aX+b line. i agree with the remainder, though :) you're right, but when i said "decrease with i" i meant just a series where Y is the value and X is the continuous axis, whgich would mean something like 1/i, where the more i grows the smaller the term becoes which asymptotes towards zero... hehe i havent done math for like 3 years :D |
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