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Type I - Lacsap's Fractions


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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 :S

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!! :gluck:

I got a, b and c (hopefully, they are correct), but when I try to formulate a general statement with them, they won't work together. I don't know what part of my process I am doing wrong, and I only have 30 hours left to work on it :(

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For the question: Let En® be the (r+1)th elements in the nth row, starting with r=0. Is this going to be a general statement with the numerator general statement over the denominator general statement. Meaning likeEn®= numberator gs/denominator gs...... or is this just the general statement for the denominator.

it doesn't ask you to do anything. basically it's just introducing what the notation En( r) represents, that's it.

in my paper i gave ever specific example possible to prove my point explained it all anyways why would i lose points, when if you do my equation it will work every single time or is it just the ib people way there are multiple ways to do it plus that equation will find you any term of the triangle oh well turned it in today~!

I don't get what you're trying to say? I can't judge how good your paper was since I had not seen it myself :lol: good luck! I hope your teacher will be pleased by it :)

I got a, b and c (hopefully, they are correct), but when I try to formulate a general statement with them, they won't work together. I don't know what part of my process I am doing wrong, and I only have 30 hours left to work on it :(

I don't know either, but you could send it to my email for me to check, if you trust me? message me if you're interested and I'll send you my email address.

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so i used the en® to help me find a formula for the denominator. so would that just be my general statement then?

not sure what you mean... your general statement is not just like En( r) and that's it, no. it has to be a function in terms of n and r.

its not allowing me to private message you :( i don't know what to do....maybe you can private message me so i can respond? or give me your email or something

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so if the formula for my denominator is my general statement, i just use that and my numerator formula to find additional rows, and do the explain the scope/limiations of both general statements or just my denominator gs?

you know basically the general statement is a formula, complete with its domain and limitations. yes to find additional rows you use the two general statements together. well the limitation must include the whole fraction.

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ok i read through all the posts and think i have the general statement for the denominator... so then i just combine it with the numerator and set it equal to En® for the general statement?

I'm really happy to hear that :)

yes that's right!

Ahh thank you so much! This really helped a lot! I think I have the full formula now!! Do you think I could send you what I think it is?

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I got 12/20 according to my teacher. I need to know the formula for the denominators. I did the Quadratic Regression and got ************* etc.. but that was the general equation?

you could have asked me for some assistance.

yes you DO need to know the formula for the denominator. you can't find it here but you can find the way to get there in this thread.

nah that is not the general equation. the general equation is an expression in terms of n and r.

note: please use n and r instead of X and whatever

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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 :S

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!! :gluck:

I got a, b and c (hopefully, they are correct), but when I try to formulate a general statement with them, they won't work together. I don't know what part of my process I am doing wrong, and I only have 30 hours left to work on it :(

so how do you do the graphical method on a calculator cuz I was just doing the Quadratic regression

Edited by M.C.RAM
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