Trikey Posted April 10, 2011 Report Share Posted April 10, 2011 so this is the new task yeah? I want a copy of the full 2013 portfolios anyway...I have also attained the same assignment and my biggest concern is how to figure out the general statement for the denominatorAlways try to make a sequence first. Look at qn 5,Let En( r ) be the (r+1)th elementh of the nth row, starting with r=0.En(1): 1, 2, 4, 7, 11En(2): 4, 6, 9Don't you see any pattern there...?Thank you very much I have figured it out now!You did? How? I figured out the rest of En2, but what good does that do? How can putting it into a sequence help? and can you hint me on how to start En(3)? Reply Link to post Share on other sites More sharing options...
Jyoti Posted April 11, 2011 Report Share Posted April 11, 2011 Hi, I'm having a great deal of trouble finding out a general statement for the denominator. I know it is somewhat connect to formula for the numerator (n^2+n)/2, but I know of nothing else. Could anyone please give me a hint or guide me in the right direction? I would really appreciate your help Reply Link to post Share on other sites More sharing options...
dessskris Posted April 11, 2011 Report Share Posted April 11, 2011 Haha sorry my explanation in post #16 was not clear enough. I was about to leave to school that's why I didn't have time to explain in long sentences. But I am sick, so I am now at home, not attending school lol. Anyway, look at the picture below:Look at all the terms in the blue area and green area. The differences are all 2 (never mind the 11). The differences from the terms in the green area and red area are also both 3 (never mind the 9).If you look at it from the left side, it's also the same. Look at the picture below:Same as above right? The terms differences between the 2nd and 3rd terms are all the same and the differences between the 3rd and 4th terms are both same too. I think this should answer all dany94's, Trikey's and Jyoti's questions (posts #17, #18 and #22). If you are still in doubt just ask again!What is meant by stating "plot En(1) against n"...what is 'against n' referring to?Sorry, plot the denominator of En(1) against n is the same as Plot y against x. Meaning denominator of En(1) (i.e. 2, 4, 7, 11) is on the y-axis and n (2, 3, 4, 5) is on the x-axis You did? How? I figured out the rest of En2, but what good does that do? How can putting it into a sequence help? and can you hint me on how to start En(3)?The pattern is exactly the same. I think what I explained above should help, but if you still don't get it please do ask, I don't mind re-explaining in a different way 5 Reply Link to post Share on other sites More sharing options...
Jyoti Posted April 11, 2011 Report Share Posted April 11, 2011 Thanks that helped me get a better understanding, but the only thing I don't seem to understand is how to turn that into a general statement using ONLY the terms n and r. I have found denominator of E subscript n-1 +(n-r), and it works perfectly, but I can't seem to change that into terms of n and r. Reply Link to post Share on other sites More sharing options...
Popular Post dessskris Posted April 11, 2011 Popular Post Report Share Posted April 11, 2011 mmm are you sure it's correct? I've just tried to work out the general statement of En(r ) and I got a quite complicated formula in terms of n and r. it did require some effort to get to the general statement.there are many ways to get to the GS but I myself used the graphical method (b/c I'm lazy...) but if you know how to find it using another method, go for it. I personally don't favour the graphical method (plotting a graph and finding the best fit curve) for a Math IA, though it's a use of technology The numerator part is very obvious and easy, right? So I don't need to discuss it.After you found the 6th and 7th rows, draw a new triangle if possible so you can see the patterns more easily.Remember that 1 is the 1st term in each row, and in this term r=0.When r=1 (the 2nd term from the left), get a table of the denominators and the n (n starts from 2). Then you find the GS for the denominator in terms of n.When r=2 (the 3rd term from the left), get a table of the denominators and the n (n starts from 3). Then you find the GS for the denominator in terms of n.When r=3 (the 4th term from the left), get a table of the denominators and the n (n starts from 4). Then you find the GS for the denominator in terms of n.Do the same thing for when r=4 and when r=5.You've got all the general statements in terms of n. Now your goal is to make them to be ONE general statement in terms of r and n.Hint: The general statement is in quadratic form (denominator=an²+bn+c)Tabulate r and the general statements. I am sure you will see some kind of pattern in the values of a, b and c. Find them with a similar method as before,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.This task is fairly easy, though it seems complicated in the beginning. Good luck to all of you!! 12 Reply Link to post Share on other sites More sharing options...
idamaria Posted April 12, 2011 Report Share Posted April 12, 2011 Thanks that helped me get a better understanding, but the only thing I don't seem to understand is how to turn that into a general statement using ONLY the terms n and r. I have found denominator of E subscript n-1 +(n-r), and it works perfectly, but I can't seem to change that into terms of n and r.i'm just wondering how n-1 + (n-r) works perfectly since for 10/7 it would be 4 - 1 + (4-1) ? maybe there is some simple thing im missing but i cant get it.. Reply Link to post Share on other sites More sharing options...
dessskris Posted April 12, 2011 Report Share Posted April 12, 2011 I have found denominator of E subscript n-1 +(n-r), and it works perfectly, but I can't seem to change that into terms of n and r.i'm just wondering how n-1 + (n-r) works perfectly since for 10/7 it would be 4 - 1 + (4-1) ? maybe there is some simple thing im missing but i cant get it.. haha it's incorrect doesn't work "perfectly"..I got a more complicated conjecture, pretty sure it works "perfectly" try to work it out yourself! if you are stuck or something just ask here, we will try to help you Reply Link to post Share on other sites More sharing options...
El Che Posted April 13, 2011 Report Share Posted April 13, 2011 The general statement applies to all row numbers and term numbers (at least it works perfectly for me). So, my question is what may be the limitations of this general statement. For example, should we try to do it with bigger numbers, or? 1 Reply Link to post Share on other sites More sharing options...
dessskris Posted April 13, 2011 Report Share Posted April 13, 2011 ^ That's also a popular question. I'd say it's something obvious:Can n and r be 0? Can they be -3? Can they be 2.5? Can they be π? Can they be √(-7)? etc etc...Express the limitation using mathematical notations. 1 Reply Link to post Share on other sites More sharing options...
glamwolf Posted April 16, 2011 Report Share Posted April 16, 2011 I found that the power function y=0.539x^1.89 is the best fit line of the data and it works as a general statement for the denominators of row 2, but thats all it can find. I put all of the n and r values in a table, but I cannot find a differnt general statement. Can anyone help lead me in the right direction? I made the table as suggested in post #25, but I cannot figure out how to get a general statement for each r value. Reply Link to post Share on other sites More sharing options...
dessskris Posted April 16, 2011 Report Share Posted April 16, 2011 a very important aspect to note: it's a quadratic function. not a power function! Reply Link to post Share on other sites More sharing options...
glamwolf Posted April 16, 2011 Report Share Posted April 16, 2011 ohhh ok! I went back into my calculator and instead of power i got the a, b, and c values for the quadratic equations. I now have the GS for each r values. I found that a stays the same, b is subtract 1, and c is add 2 plus the previous number added excpet it doesn't work for r=2. i can only find a GS for the b and c value it says math error when i try to do the a values. how would i combine those 3 GS into one? Help is much appreciated. Thanks so much Reply Link to post Share on other sites More sharing options...
dessskris Posted April 17, 2011 Report Share Posted April 17, 2011 well if the a stays the same why would you need to find its value using calculator? hmm just a little hint:the expression of b in terms of r is linearthe expression of c in terms of r is quadratichow to find the expression? same method as before.. 2 Reply Link to post Share on other sites More sharing options...
redsmartie Posted April 17, 2011 Report Share Posted April 17, 2011 i found a formula to determine the numerator and demoninator, but they are simple equations and none are quadratic formulas, however they work for every case.am i wrong? or is it possible for more than one answer or general formula? Reply Link to post Share on other sites More sharing options...
El Che Posted April 19, 2011 Report Share Posted April 19, 2011 The general statement, for both numerator and denominator, should be quadratic. I've got back my portfolio and my teacher approved the formula I found, so I assume that it is the right and the only one (in my opinion). Reply Link to post Share on other sites More sharing options...
dessskris Posted April 19, 2011 Report Share Posted April 19, 2011 @redsmartie what do they look like? are they expressed in terms of n and r or in terms of the previous term? I would agree with Gestapo, there is one and only one general statement. Reply Link to post Share on other sites More sharing options...
aangel Posted April 28, 2011 Report Share Posted April 28, 2011 Isn't it the numerator we are trying to find. Reply Link to post Share on other sites More sharing options...
glamwolf Posted April 29, 2011 Report Share Posted April 29, 2011 (edited) Ok I found the equation for the denominator. It looks right but i can't seem to plug in the numbers and get the right denominators. What am I doing wrong? I found the equation by plugging in the tables for each value a, b, and to get an equation for each and then I combined them to get that equation. It looks right, because the a value stays the same. The b value goes down by one and the c value is the r value squared. I can't prove it though, Am I doing it wrong? Do I have to use both the row number and r value and if so which one goes where. Thanks for the help Edited April 30, 2011 by glamwolf Reply Link to post Share on other sites More sharing options...
glamwolf Posted April 29, 2011 Report Share Posted April 29, 2011 Isn't it the numerator we are trying to find.You need to find an equation for the numerator first and then find one for the denominator. I haven't finished yet, but I assume you then put the two equation on top of each other to get a general statement for the whole fraction. Reply Link to post Share on other sites More sharing options...
dessskris Posted April 30, 2011 Report Share Posted April 30, 2011 @aangelnumerator first and then denominator. exactly what glamwolf said. @glamwolffirst of all could you please remove that equation from your post?? thanks!and yup you need to use both r and n, that's why I said the denominator formula should be in terms of r and n. well what do you think, where to put the r? you need to think! think!! I can't keep giving you hints as I've given a lot of ones think... and get it right!PS. if you really really don't know, I'll try to guide you. Reply Link to post Share on other sites More sharing options...
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