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Type I - Lacsap's Fractions


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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?

thanks :) glad to hear that!

oh sorry, you need to first get the expression of denominator in terms of n for each value of r (at least 3 values of r, ideally 5) and then from those 3 or 5 formulas, you should see a pattern for each of a, b and c, and then express each in terms of r and combine them all together.

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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:

how do you find generalize it though? like what does that mean? i have five statements, but i don't know what to do with them
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how do you find generalize it though? like what does that mean? i have five statements, but i don't know what to do with them

basically generalise means try as much to make the numbers (constants) become variables which work for all n and all r (not only certain values of n and r). good that you have 5 statements. now look at each one of them, can you see any pattern in the values of a, b and c? if so, now generalise it. find the expression of each in terms of r and just combine them at the end.

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how do you find generalize it though? like what does that mean? i have five statements, but i don't know what to do with them

basically generalise means try as much to make the numbers (constants) become variables which work for all n and all r (not only certain values of n and r). good that you have 5 statements. now look at each one of them, can you see any pattern in the values of a, b and c? if so, now generalise it. find the expression of each in terms of r and just combine them at the end.

is there a way that i can show you my 5 statements so tha tyou can tell me if they are correct?
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is there a way that i can show you my 5 statements so tha tyou can tell me if they are correct?

ok you can send them to me through a message just to check :)

how do you do that?

it says that i do not have enough posts to send a message so i am going to write random things to count it as a post.

the internal is hard.

ahhh junior year, the IB =/

it says that i need to have at least five posts.

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Ok everyone ive read and ive done my ib project the only problem is i can't explain how i got this equation to find the term you are seeking , it finds both the denominator and numerator *******************

so if u plug it in you can find any term you need r = row and c = column = term ex: 3/2 would be collumn 2 row 2

If you need the seperate equations that i have for the denominator and numerator i can post that

Some one help me its due tommorow !

Edited by Mahuta ♥
Do not give any answers please.
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hi im so confused with the denominator part... is there suppose to be a different formula for every row?

in terms of n, yes different formulae. but generally, there's one big general statement in terms of n and r which works for all rows.

how many points am i going to lose if i turn it in like that i have thoroughly explained my method ,drawn diagrams and proven examples given that my formula for the triangle to late for me to change it oh well

could be about 2... depends on how good the rest of your paper is.

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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.

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hi im so confused with the denominator part... is there suppose to be a different formula for every row?

in terms of n, yes different formulae. but generally, there's one big general statement in terms of n and r which works for all rows.

how many points am i going to lose if i turn it in like that i have thoroughly explained my method ,drawn diagrams and proven examples given that my formula for the triangle to late for me to change it oh well

could be about 2... depends on how good the rest of your paper is.

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~!

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