Maths coursework
In this coursework we were asked to find the differences in a simple fraction pattern. We had ;
I will look at the differences between the fractions and search for any general rules. I will apply my good algebraic skills to help find any rules.
I then had to find the differences by taking the fractions away from each other. To find my first difference I had to ;
D1 = difference one
Fraction 2nd-1st 3rd-2nd 4th-3rd
D1 1st 2nd 3rd
I had to take away 2/3 form 1/2 but the denominators were not the same, so I found the lowest common multiple from each and multiplied them top and bottom eg.
X2 2 - 1 X3
X2 3 2 X3
The lowest common multiple is 6 so I multiplied 2/3 by 2 and 1/2 by 3. I then got ;
4/6 - 3/6 which then equalled 1/6, which was my 1st difference.
I done the same to 3/4 - 2/3 9/12 – 8/12 which equalled 1/12 and my second difference.
I shall begin to search for an algebraic rule for the first differences
To find the nth term I had to take away the n+1th term away from the nth term ;
n+1 – n
n+2 n+1
I made the denominators the same and got ;
(n+1)(n+2) - n(n+2)
(n+1)(n+2) (n+1)(n+2)
I then multiplied the brackets out by completing the square. For the numerator
