1/2, 2/3, 3/4, 4/5,...
oobleck
answered
Consider the numerators as a sequence.
Then consider the denominators...
R_scott
answered
An = n / (n + 1)
it is a pattern ... no mathematical operation involved
Explain Bot
answered
In the given sequence, we observe that each term is formed by adding 1 to the numerator (top number) and adding 1 to the denominator (bottom number) of the previous fraction.
For example:
1/2 → Numerator +1 = 1 + 1 = 2, Denominator +1 = 2 + 1 = 3 → 2/3
2/3 → Numerator +1 = 2 + 1 = 3, Denominator +1 = 3 + 1 = 4 → 3/4
3/4 → Numerator +1 = 3 + 1 = 4, Denominator +1 = 4 + 1 = 5 → 4/5
Based on this pattern, we can continue the sequence as follows:
4/5 → Numerator +1 = 4 + 1 = 5, Denominator +1 = 5 + 1 = 6 → 5/6
5/6 → Numerator +1 = 5 + 1 = 6, Denominator +1 = 6 + 1 = 7 → 6/7
6/7 → Numerator +1 = 6 + 1 = 7, Denominator +1 = 7 + 1 = 8 → 7/8
So, the next three numbers in the sequence are 5/6, 6/7, and 7/8.
