dessskris Posted April 15, 2011 Report Share Posted April 15, 2011 When the portfolio tells us to "Define Tn (a,x)" we simply define it and do nothing more, correct?note: I have Pro-D day tomorrow, so I have no way to contact my teacher.Secondly when I use my observations from the "investigations" to find teh general statement of the infinite sum,do I simply state it or must I provide work on how I achieved the general statement or general solution of "Sn=x^a"?Yes, simply define it.Show all your working and calculations.If there is any doubt you can just ask us here! Reply Link to post Share on other sites More sharing options...
Daniel Inchan Jung Posted April 15, 2011 Report Share Posted April 15, 2011 (edited) Thank you for confirming Desy.Now the final aspect of this IA that is worrying me is how one comes up withthe general solution - which many people claim - to be Sn = a^x.How does one come up with that?One person explains it as t1=(x ln a)/1, the x is just pulled out from it's actual exponential spot.Could someone help nudge me into the right direction?note: Please do not suggest Taylor and Maclaurin series unless the logic behind it can be explained thouroughly. Edited April 15, 2011 by Daniel Inchan Jung 1 Reply Link to post Share on other sites More sharing options...
wombat123 Posted April 16, 2011 Report Share Posted April 16, 2011 So for the second part of the IA, where they say to use different values of a where x=1, I'm not sure as to what the purpose of that command is. Are they trying to have us explore further examples to prove the relation between Sn and n which we established in the first part of the portfolio? If so, isn't that a bit too...straightforward? Because in that case the only thing I can think of doing is to try increasing the value of a like, three-four times. Many thanks to the person who helps this poor soul. Reply Link to post Share on other sites More sharing options...
Daniel Inchan Jung Posted April 16, 2011 Report Share Posted April 16, 2011 So for the second part of the IA, where they say to use different values of a where x=1, I'm not sure as to what the purpose of that command is. Are they trying to have us explore further examples to prove the relation between Sn and n which we established in the first part of the portfolio? If so, isn't that a bit too...straightforward? Because in that case the only thing I can think of doing is to try increasing the value of a like, three-four times. Many thanks to the person who helps this poor soul.The purpose of that command is to guide you towards the restrictions or limitations of the general solution you have already come up with. 1 Reply Link to post Share on other sites More sharing options...
dessskris Posted April 16, 2011 Report Share Posted April 16, 2011 Thank you for confirming Desy.Now the final aspect of this IA that is worrying me is how one comes up withthe general solution - which many people claim - to be Sn = a^x.How does one come up with that?One person explains it as t1=(x ln a)/1, the x is just pulled out from it's actual exponential spot.Could someone help nudge me into the right direction?note: Please do not suggest Taylor and Maclaurin series unless the logic behind it can be explained thouroughly.well, you have the values of Sn when x=1 and a=2, when x=1 and a=3, and when x=1 and for some other values of a. so you can derive the formula of Sn in terms of a when x=1 from there.I think what you mentioned is S∞, not Sn.then you have T9 (which is the same as Sn, right?) when a=2 for various values of x. so find the expression for T9 when a=2. do the same when a=3, a=4, etc. then you find the general statement of T9 in terms of a and x.repeat that with some other values of n and you will finally find Tn in terms of a and x.or if you look at the Taylor Expansion formula in the equations in Ms. Word, you will notice that the x in your formula is a special something in your task. you will then be able to find S∞ using that formula.So for the second part of the IA, where they say to use different values of a where x=1, I'm not sure as to what the purpose of that command is. Are they trying to have us explore further examples to prove the relation between Sn and n which we established in the first part of the portfolio? If so, isn't that a bit too...straightforward? Because in that case the only thing I can think of doing is to try increasing the value of a like, three-four times. Many thanks to the person who helps this poor soul.It's to guide you to get the general statement step by step. Reply Link to post Share on other sites More sharing options...
birdman Posted April 18, 2011 Report Share Posted April 18, 2011 I was given the type I of the math portfolio and it has to do with infinite summation. The formula we are using is (xlna)^n/n!. I am doing the first part of the task, and now i have to find general statement that represents the infinite sums of the general sequence. Is it just a^x should i just write that and just continue to the next part of the portfolio?please help??!The type 1 is in the attachment!GetFile.pdf Reply Link to post Share on other sites More sharing options...
julianhallems Posted April 19, 2011 Report Share Posted April 19, 2011 Could someone help me understand the Taylor and Maclaurin series? I've finished my first draft for the portfolio but I'm really looking to beef it up further. any help on this is much appreciated! Reply Link to post Share on other sites More sharing options...
dessskris Posted April 22, 2011 Report Share Posted April 22, 2011 I was given the type I of the math portfolio and it has to do with infinite summation. The formula we are using is (xlna)^n/n!. I am doing the first part of the task, and now i have to find general statement that represents the infinite sums of the general sequence. Is it just a^x should i just write that and just continue to the next part of the portfolio?please help??!The type 1 is in the attachment!The first part is when x=1, right? I think if so you wouldn't get ax yet, you would only get a because x=1. Then when x varies, you would notice that it's ax.Could someone help me understand the Taylor and Maclaurin series? I've finished my first draft for the portfolio but I'm really looking to beef it up further. any help on this is much appreciated!TBH I haven't covered those in IB yet but when you see the Taylor Expansion formula in the equations in Ms. Word, you will notice that the x in your formula is a special something in your task. You will then be able to find S∞ using that formula.If still not clear, please do ask. Reply Link to post Share on other sites More sharing options...
Guest JimmyK Posted April 23, 2011 Report Share Posted April 23, 2011 Just read the first 5 pages of this topic and didn't help me a lotYou see, I'm quite confused right now because of all the opinions that are here posted... I have been doing my IA with the common ratio of xlna/n. I believe it is the common ratio as it applies to all of the terms. For t0, you get 1 and if you multiply it by this expression, you'll get the second term. Multiplying this second term by the expression will give you the third term and so on. The only thing is that using the general expression of geometric series (un = u1 x common ratio). Because you have to have a factorial of n in the denominator instead of just n. Thus, I don't get how people say that the general expression is ax ... I've seen the Taylor expression but can't get how you reach it.I have no idea of whether my results are correct or not because I've been using GDC to calculate the Sn through the formula Sn = (1 - rn)/(1 - r) and it has always given me something converging to 1... :|If anyone could help me by just giving me some few guidelines, I'd appreciate it. Just please, explain why you're giving that specific guideline... Reply Link to post Share on other sites More sharing options...
dessskris Posted April 23, 2011 Report Share Posted April 23, 2011 I’ve never read the first 5 pages of this thread either, but please do read the whole thread if you have the time to. I remember discussing this before but not really in detail. So now I am going to explain it to you in great detail.I hope it’s clear enough. Otherwise you just need to read between the lines jk, otherwise please do ask here. I am trying to help you but I cannot give too much help, I can only guide you to the right direction, and I believe that is what I have always done if you are still in doubt please do ask again. Reply Link to post Share on other sites More sharing options...
Guest JimmyK Posted April 23, 2011 Report Share Posted April 23, 2011 I’ve never read the first 5 pages of this thread either, but please do read the whole thread if you have the time to. I remember discussing this before but not really in detail. So now I am going to explain it to you in great detail.I hope it’s clear enough. Otherwise you just need to read between the lines jk, otherwise please do ask here. I am trying to help you but I cannot give too much help, I can only guide you to the right direction, and I believe that is what I have always done if you are still in doubt please do ask again.I got that part lol and it's quite easy to understand that. But the question is how do you get a result such as ax?? I cannot really understand how you can convert something that is lnx into ax without having to put an e (Euler's number)...that's my questionps: Just to point that common difference is in an arithmetic progression. Common ratio is the correct expression for geometric ones Reply Link to post Share on other sites More sharing options...
dessskris Posted April 23, 2011 Report Share Posted April 23, 2011 hmm..what about you start doing it first. if you don't get ax in the end then ask here.remember that ln(x)=loge(x)and that a^(loga(b))=bOH hahahaha right thank you for pointing that out! you mentioned something about common difference that's why I was kind of dragged into talking about it lolhmm..what about you start doing it first. if you don't get ax in the end then ask here.remember that ln(x)=loge(x)and that a^(loga(b))=bOH hahahaha right thank you for pointing that out! you mentioned something about common difference that's why I was kind of dragged into talking about it lol Reply Link to post Share on other sites More sharing options...
Guest JimmyK Posted April 23, 2011 Report Share Posted April 23, 2011 (edited) hmm..what about you start doing it first. if you don't get ax in the end then ask here.remember that ln(x)=loge(x)and that a^(loga(b))=bOH hahahaha right thank you for pointing that out! you mentioned something about common difference that's why I was kind of dragged into talking about it lolhmm..what about you start doing it first. if you don't get ax in the end then ask here.remember that ln(x)=loge(x)and that a^(loga(b))=bOH hahahaha right thank you for pointing that out! you mentioned something about common difference that's why I was kind of dragged into talking about it lolahah but that was to say that it wasn't an arithmetic one lolAs for the other part, I've tried but still can't get it how it equals ax. It cannot be simply ax... you have to equal lnx to something to transform it into another expressionyou have to have lnx = y to say that ey = x, right or wrong? o.Oit's either that or my maths is not very good atm... Edited April 23, 2011 by JimmyK Reply Link to post Share on other sites More sharing options...
dessskris Posted April 23, 2011 Report Share Posted April 23, 2011 yeah I meant I should have said common ratio instead.yes yes you need to do some 'mathematical manipulations' to finally arrive at ax. remember all the rules you were taught in the log chapter. Reply Link to post Share on other sites More sharing options...
Guest JimmyK Posted April 23, 2011 Report Share Posted April 23, 2011 yeah I meant I should have said common ratio instead.yes yes you need to do some 'mathematical manipulations' to finally arrive at ax. remember all the rules you were taught in the log chapter.Right... I'm going to see what I can figure out from the log rules... :| *scared* ahahha Reply Link to post Share on other sites More sharing options...
aronnax Posted April 25, 2011 Report Share Posted April 25, 2011 If someone could help me out, I'll be grateful.The question asked for a General Statement.Now, I know that this is a formula of some sort which I haven't figured out yet, but what about the first time they asked for the general statement on the last paragraph of the last page.Is there a formula I need to put there too? Because I put: The general statement is:The value of infinite summation in the sequence tn will never be greater than the value of the number a in the sequence equation of (x ln (a))^n/n! or in other words, Sn ≤ a Reply Link to post Share on other sites More sharing options...
dessskris Posted April 26, 2011 Report Share Posted April 26, 2011 remember that this is a Mathematics portfolio, therefore your general statement (GS) must be in the form of a formula. please note that they are asking for the infinite sum, so they want S∞ not just Sn till n=10.actually your GS is almost correct. you need to state the conditions too. Reply Link to post Share on other sites More sharing options...
Magnus Posted April 26, 2011 Report Share Posted April 26, 2011 (edited) How many, and what values of a is recommended when variating the different values of a at the first general statement?i've chosen 4, 15, and 23. But should i include more than three? and should i have more exotic numbers like sqrt5, 142/13 and so on...? Edited April 26, 2011 by Magnus Reply Link to post Share on other sites More sharing options...
dessskris Posted April 26, 2011 Report Share Posted April 26, 2011 you've got 2 values, right? when a=2 and when a=3. I suggest having 3 more (so in total you have 5 different values of a).good! I suggest various forms of number like √k, fractions, sin(k), π, e, or i (do you learn complex numbers in Math SL? if not never mind i) 1 Reply Link to post Share on other sites More sharing options...
aronnax Posted April 26, 2011 Report Share Posted April 26, 2011 Ah thanks dessskris. It helped! Reply Link to post Share on other sites More sharing options...
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