dessskris Posted November 23, 2011 Report Share Posted November 23, 2011 This was the most helpful post for me. Thank you very much, even though I had figured out these patterns, you really helped me "materialize" it. This is probably the best method of finding the general statement, as it provides plenty of opportunities to use technology. Again, thanks glad to hear that you're welcome!! @tata123 basically just do that ^ Reply Link to post Share on other sites More sharing options...
sarawr Posted November 24, 2011 Report Share Posted November 24, 2011 hey, so i was just wondering, what are some points to mention in the introduction to this IA? I'm a little stuck on what I should say. Also, did any of you use graphs to illustrate how you got the answer because i didnt use a single one but im not sure if i should just put one in there anyways?? any thoughts? Reply Link to post Share on other sites More sharing options...
dessskris Posted November 24, 2011 Report Share Posted November 24, 2011 hey, so i was just wondering, what are some points to mention in the introduction to this IA? I'm a little stuck on what I should say. Also, did any of you use graphs to illustrate how you got the answer because i didnt use a single one but im not sure if i should just put one in there anyways?? any thoughts?not much, just briefly introduce what your task is all about, then show the triangle.well if you used a graphical method to find the general statements, meaning you use regression thing from your calculator, YES you DO need to include the graphs. but if you found the general statements purely by algebra then don't need to use graphs..however, the first part of the task asks you to plot the numerator against n, right? so you have no choice, you MUST include at least one diagram in this portfolio, which is this one. Reply Link to post Share on other sites More sharing options...
CharlotteW Posted November 26, 2011 Report Share Posted November 26, 2011 Has anyone had any luck proving the general statement using the principal of mathematical induction? Reply Link to post Share on other sites More sharing options...
dessskris Posted November 26, 2011 Report Share Posted November 26, 2011 no you cannot prove it using maths induction, for various reasons that I can't explain my mind just tells me this can't be proved through maths induction. however, there is a formal proof for the formula of each diagonal. Reply Link to post Share on other sites More sharing options...
CharlotteW Posted November 26, 2011 Report Share Posted November 26, 2011 See, I've tried that, but it's just not working for some reason Reply Link to post Share on other sites More sharing options...
dessskris Posted November 26, 2011 Report Share Posted November 26, 2011 of course not... maths induction is not used to prove this kind of thing Reply Link to post Share on other sites More sharing options...
Vincent268 Posted November 26, 2011 Report Share Posted November 26, 2011 Thanks god, you all really helped me! Thanks!Vinc, IB Canada Reply Link to post Share on other sites More sharing options...
Dreamzman Posted November 26, 2011 Report Share Posted November 26, 2011 Get a table of a and r. Then you find the GS for a in terms of r. Get a table of b and r. Then you find the GS for b in terms of r. Get a table of c and r. Then you find the GS for c in terms of r. So you've got a, b and c. Put them in the general statement involving n. You will get the GS for the denominator in terms of n and r. Desy, I'm curious as to what you meant by the quote above. Do you mean to literally find a GS for a/b/c in terms of r and find the zero, or am I missing something here? sorry if it wasn't clear. I mean: tabulate the values of a and r. then, try to find an expression of a in terms of r. for example: (note that this is a totally random example) same thing for b and c. do you get it? once you are done, for example this is what you get: (again, note that this is a totally random example) I hope that was clear enough. any question just ask. Thank you so much for all of your help! You've really helped me get through this IA. I just have one question about the GS. I understand that it is supposed to be a quadratic, but I don't quite understand the above method. Which values do you plug into a chart for a,b,and c? BUT WHAT IS A or B or C .. and do i use my calculator to table this ? how do u do this. what do i put in my calculator.. PLEASE HELP Reply Link to post Share on other sites More sharing options...
hehe_lalalala Posted November 26, 2011 Report Share Posted November 26, 2011 I actually found that a cubic regression works best for the numerator's relation with the row number...I'm still having trouble with the denominator, though, can someone please explain? Reply Link to post Share on other sites More sharing options...
arslansaeed Posted November 27, 2011 Report Share Posted November 27, 2011 ok so En(1)= 1,2,4,7,11,16 so plot that against 1,2,3,4,5,6 on your calculator(Ti-83) and then quad reg it, do i do that with all up to En(5) then generalize 1 Reply Link to post Share on other sites More sharing options...
hehe_lalalala Posted November 27, 2011 Report Share Posted November 27, 2011 (edited) Thanks for clearing that up! I was just unsure what to plot the denominators against. So the graph is basically row number and denominator? and then I quad reg?EDIT: Another question about the logistics of plotting row against denominator.. do I just keep decreasing the number of rows in the list I'm plotting since the starting row decreases each time and the number of denominators decreases, too? Does that make sense? Sorry if it doesn't. $: Edited November 27, 2011 by hehe_lalalala Reply Link to post Share on other sites More sharing options...
dessskris Posted November 27, 2011 Report Share Posted November 27, 2011 BUT WHAT IS A or B or C .. and do i use my calculator to table this ? how do u do this. what do i put in my calculator.. PLEASE HELP you have the values of a, b and c. you are to find the formula of a, b and c in terms of r. yeah you can use your calculator. do it separately: a and r, b and r, and c and r. I actually found that a cubic regression works best for the numerator's relation with the row number... nah it's quadratic. in IA Type 1, there is only one correct answer. unlike in IA Type 2, where there can be various answers and there's no "answer key" Thanks for clearing that up! I was just unsure what to plot the denominators against. So the graph is basically row number and denominator? and then I quad reg? yes EDIT: Another question about the logistics of plotting row against denominator.. do I just keep decreasing the number of rows in the list I'm plotting since the starting row decreases each time and the number of denominators decreases, too? Does that make sense? Sorry if it doesn't. $: I don't get what you mean. for example the data is like this: row: 2 3 4 denominator 1 3 7 you can put (2,1) first in the table and (3,3) second and (4,7) last, or in any kind of order you like because in the end when you put it in a graph, the computer will place the data in the correct order. Reply Link to post Share on other sites More sharing options...
arslansaeed Posted November 27, 2011 Report Share Posted November 27, 2011 can you explain what we are doing when we plot the E(1) or any of the r's against n are we looking for the regression? what equation are we looking for? Reply Link to post Share on other sites More sharing options...
dessskris Posted November 27, 2011 Report Share Posted November 27, 2011 (edited) yep, you're formulating the denominator for each diagonal block. Edited November 27, 2011 by Desy Glau Reply Link to post Share on other sites More sharing options...
arslansaeed Posted November 27, 2011 Report Share Posted November 27, 2011 ya but what exactly am i doing to the table, am i going to quadreg it? quadreg all 5 then generalize all the equations? Reply Link to post Share on other sites More sharing options...
dessskris Posted November 27, 2011 Report Share Posted November 27, 2011 yes correct. Reply Link to post Share on other sites More sharing options...
hehe_lalalala Posted November 27, 2011 Report Share Posted November 27, 2011 I don't know why/how a cubic works best for my numerator, it passes through all the points and my quadratic doesn't...so it's messing with the part where I have to find the GS for the denominator, because I've been following the method outline here, which uses a quadratic method. Should I redo everything with cubic regressions, or change my numerator GS to quadratic? Reply Link to post Share on other sites More sharing options...
dessskris Posted November 27, 2011 Report Share Posted November 27, 2011 no, there's no rule saying your numerator has to be in a similar form as the denominator. keep your denominator as quadratic.now, uhm, you sure a quadratic doesn't work in the numerator? maybe you put your data wrongly? can you show me your table? Reply Link to post Share on other sites More sharing options...
hehe_lalalala Posted November 27, 2011 Report Share Posted November 27, 2011 I used a graphing caluculator.In "L1" for stat plot I inputted 1,2,3,4 and 5 for the rows.In "L2" I inputted 0, 3, 6, 10 and 15 for the numerators.When I did this, I then tested for linear, quadratic, cubic, and quartic regressions. Cubic passed through all the points whereas quadratic didn't, so I assumed that it was cubic.However, later on when I was trying the denominator GS, I noticed that a quadratic actually ends up following the trend better than the cubic.SO did I do the regression right? And if I did, should I include my findings later on about how quadratic might work better? Reply Link to post Share on other sites More sharing options...
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