Question:I'm looking for help in finding the original equation behind a set of given answers:

whenx = 100, the answer is0.5(1/2)

whenx = 200, the answer is0.6666(2/3rds)

whenx = 300, the answer is0.75(3/4ths)

whenx = 400, the answer is0.8(4/5ths)

There is a pattern, and I tried approaching this problem as a Sequence, but could not get the differences to converge.

I cheated, and found the hidden formula(shown below)which governs the above sequence, but I still want to know how to reverse-engineer this problem so I could have found the "Hidden Formula" without looking up the answer.

Hidden Formula:x ÷ (x + 100)

so when x = 100, the formula would be: 100 ÷ (100 + 100) = 100 ÷ 200 = 0.5

Thank you for any help you can give.