Patterns With Fractions Investigations

The first 200 words of this essay...

Mathematics Coursework.

Patterns With Fractions.

Consider the sequence of fractions and the differences between the fractions:

Term (n) 1 2 3 4 5

1st Difference

2nd Difference

(For rest of differences, see page11)

Finding the starting fraction for the nth term:

, , , , = (The general formula)

Check if correct formula:

Term

(n)

Numerator

(n)

Denominator

(n + 1)

Final

Fraction

1

1

2

?

2

2

3

?

3

3

4

?

4

4

5

?

5

5

6

?

(Check On Page 11)

Finding the nth term for the 1st difference:

In order to find out the nth term for the 1st differences, the requirement is to subtract the 2nd fraction from the 1st fraction (the smaller fraction from the bigger fraction).

-

=

=

= (The general formula