IA Type I - Lacsap's Fractions

[El Che]

E_n(r) = [n(n+1)]/[n(n+1)+2r(r-n)]

amidoinitrite?

I would suggest you don't share your answers. It's forbidden according to the rules of the forum. But I'll answer your question: No, it's not right.

Do i use the general statement En® to find the eight and ninth row for the question about finding additional rows? How many more additional rows are needed to find for the question?

Well, once you have the formula you can check whether your general statement works for eighth and ninth rows. In fact, finding up to seventh row, as the task suggests, is enough.

Edited December 12, 2011 by El Che

[Guest]

Hello, i really need help on this.

for the "using technology, plot the relation between the row number and the numerator in each row", we can use a graphic calculator right?

I tried using the steps and searched online for help on the quadratic regression, but i still don't get how i'm supposed to insert my numbers in into the calculator.

Is there some other ways where i can do this? like on excel or something?

Can someone help me on this? Thanks!

[El Che]

Hello, i really need help on this.

for the "using technology, plot the relation between the row number and the numerator in each row", we can use a graphic calculator right?

I tried using the steps and searched online for help on the quadratic regression, but i still don't get how i'm supposed to insert my numbers in into the calculator.

Is there some other ways where i can do this? like on excel or something?

Can someone help me on this? Thanks!

Yes, you can use your calculator. Which GDC do you use? I can give you instructions on TI-84.

For entering the values into the lists:

1. Press [sTAT] button.
   
2. Choose [Edit].
   
3. A screen will appear and you will see the following lists: L1, L2, L3
   
4. Enter your values in L1 and L2.
   

For using the regression tool:

1. Press [sTAT] button.
   
2. Use your right arrow and move to [CALC] menu.
   
3. Scroll down until you find QuadReg.
   
4. Press [ENTER].
   
5. It will appear on the calculator's screen.
   
6. Execute it by pressing one more time on [ENTER].
   

[El Che]

Thank you so much! i got 0.5 for both L1 & L2 and do you know how i am supposed to explain this? What is this number for?

I just read from the previous post that i can use this way as one type of technology but i don't get what i'm finding for.

Also, if i want to write a general statement to represent the numerator, do i just put it as En & not En®?

Btw, have you tried for values up to r = 4? I mean putting the corresponding numbers in L1 and L2 when r = 1, r = 2, and s o on. Once you do that, there will appear a pattern which will ease your work to generalize the statement, considering the values obtained for a, b, and c. I'd suggest you tabulate them at first. Then, by looking at them you will see if any of the constants changes (increase or decrease) at different r, or stays the same. After that you substitute those values in the quadratic equation formula and you're good. You put it as E_n®. Let me know if I'm not clear enough. Good luck!

[Johnny Bisen]

@El Che

E_n(r) = [n(n+1)]/[n(n+1)+2r(r-n)] = [n(n+1)]/[(n-r)(n-r+1)+r(r+1)]

[AndAMinorInHistory]

I just do not understand how we are to generalize the r equations.

[Wendy Fong]

anyone use the combinations method to solve the questions?

[Guest]

Btw, have you tried for values up to r = 4? I mean putting the corresponding numbers in L1 and L2 when r = 1, r = 2, and s o on. Once you do that, there will appear a pattern which will ease your work to generalize the statement, considering the values obtained for a, b, and c. I'd suggest you tabulate them at first. Then, by looking at them you will see if any of the constants changes (increase or decrease) at different r, or stays the same. After that you substitute those values in the quadratic equation formula and you're good. You put it as E_n®. Let me know if I'm not clear enough. Good luck!

Oh i think i get you, i did that for values up till 4 and i saw that pattern. But what is this finding for? the formula for the numerator?

[El Che]

Oh i think i get you, i did that for values up till 4 and i saw that pattern. But what is this finding for? the formula for the numerator?

It's for the denominator.

[Guest]

It's for the denominator.

omg yes.. cause my IA is due tmr so my mind is so messy now. Thanks!

But what does the ax_² + bx + c means? do i plug in the numbers i get for the a,b and c into it?

im really confused with this equation. i don't know what i need to do with it...

[El Che]

omg yes.. cause my IA is due tmr so my mind is so messy now. Thanks!

But what does the ax_² + bx + c means? do i plug in the numbers i get for the a,b and c into it?

im really confused with this equation. i don't know what i need to do with it...

Yes. If you have figured out the pattern, you just plug in those values of a, b, and c into the equation and you're ready! =)

[Guest]

Oh and can someone explain to me, if i graphed out the numerator, how do i tell if it's a quadratic equation?

I just know that the numerator is a quadratic equation because of the second level common difference.

[El Che]

Oh and can someone explain to me, if i graphed out the numerator, how do i tell if it's a quadratic equation?

I just know that the numerator is a quadratic equation because of the second level common difference.

Finding the expression for the numerator is way easier than the denominator.

Here is a simple hint: Just search for "triangular numbers" in the Internet and find their formula. Then plug in some numbers to see whether it satisfies the numerators in the first rows. For example, try with 5 and see if you get 15 in the end. =)

[Guest]

Finding the expression for the numerator is way easier than the denominator.

Here is a simple hint: Just search for "triangular numbers" in the Internet and find their formula. Then plug in some numbers to see whether it satisfies the numerators in the first rows. For example, try with 5 and see if you get 15 in the end. =)

yea i know that the expression for the numerator is really easy and i've got it. it's just the graph that made me really confuse..

for the numerator, actually i get it, its just i don't know how i should present my work.

now im moving on to the denominator part. it's so confusing, i tried rereading the suggestions people gave here but im still stuck..

how do i exactly find the expression of the denominator for r=1,r=2,r=3?

[jag913a]

it's okay just be careful next time!

note that I'm not doing this task for my IA, so don't worry I won't take your equations or plagiarise or whatever

that's okay, not a problem

did you follow the procedure I suggested? if yes:

when r=1 you get an equation in terms of n.

when r=2 you get another equation in terms of n.

when r=3 you get yet another equation in terms of n.

etc.

then when you generalise the r, you get one GENERAL equation in terms of n and r.

do you get it now?

How do you generalize r. I'm obtaining the equation in terms of n, but I don't understand how to take that and make it into terms of n and r by generalizing r? Please help me, I've been going throught this forum for two hours and I just need to understand this and I'll be good. Please and thank you!

[Mcow1993]

I am currently doing this as well. I have very little clue about what to do. I have the numerator, but i'm having trouble with the denominator :/ I've read a bunch of posts on this topic but their not helping much. Really doesn't help that the best calculator that I have available to me here at home is a scientific calculator. I have no idea how to use it with this. I doubt it can help me. I really feel like I'm drowning here, and this is due tomorrow. Seeing my limited calculator use, can someone give me fast advice on how to deal with this?

[dessskris]

for r=5 to find a general statement is it linear regression because it says error with the quadratic regression

everything is quadratic. if your r=5 does not fit with the general statement then your data is wrong.

anyone use the combinations method to solve the questions?

that won't work.

How do you generalize r. I'm obtaining the equation in terms of n, but I don't understand how to take that and make it into terms of n and r by generalizing r? Please help me, I've been going throught this forum for two hours and I just need to understand this and I'll be good. Please and thank you!

you must've lied, if you went through this thread you must've seen where I explained how to generalise r. for god's sake, I had explained it more than once! surely if one goes through the whole thread, one must've realised that I've repeated the whole thing over and over and over and over.....

I am currently doing this as well. I have very little clue about what to do. I have the numerator, but i'm having trouble with the denominator :/ I've read a bunch of posts on this topic but their not helping much. Really doesn't help that the best calculator that I have available to me here at home is a scientific calculator. I have no idea how to use it with this. I doubt it can help me. I really feel like I'm drowning here, and this is due tomorrow. Seeing my limited calculator use, can someone give me fast advice on how to deal with this?

if you think I'm not helping much then get your teacher to help you. for god's sake I don't get paid for this and if all you're going to tell me is that I'm not helpful, well go somewhere else and find more helpful people. like those mathematicians from India who can do this portfolio for you if you pay them.

I hope you know that you MUST have a graphic display calculator for your exams.

but for god's sake this task can be done without a GDC with the same tips. surely you have a computer with Microsoft Excel? if not then well just fail this IA.

[opus92fan]

I attempted to use a systems of equations to find the equation of the general statement, it worked for the numerator but not for the denominator.

[Frankie91493]

I have also attained the same assignment and my biggest concern is how to figure out the general statement for the denominator

This may be a bit late, but to find the numerator: Create a table with x as the row, and y as the numerator. Pick any diagonal column (ie, 1, 3/2, 6/4, 10/7, 15/11) and put the data in it. See if your calculator can find any correlation between the two. Also, try finding the different between the numerators to the second level (ie, level one is: 3 - 1 = 2, 6 - 3 = 3, 10 - 6 = 4, 15 - 10 = 5, and level two: 5 - 4 = 1, as does 4 - 3, 3 - 2, and 2 - 1). Look at what you get from doing this, and try use any correlations to find the next few rows.

This should push you in the right direction, and can be used if you replace the numerators with denominators…

[kderby]

I see all the patterns in the triangle and have noticed some little formulas i can use with only n and r, but what is really stumpping me is the E in the equation in question 5. Is there any significance it being there? I don't understand what it stands for. Can someone plz try to explain it .?