The relation is this: Take the numbers from 1 to 10 (and beyond, but 1 to 10 works fine for an example) and map them in the following way:

2/1, 3/2, 4/3, 5/4, 6/5, 7/6, 8/7, 9/8, 10/9

This gives you the factors between step, i.e. the proportionality for how much magnitude is actually gained by each step. Put simply, the factor between each step can easily be expressed as x/(x-1).

If you'd multiply all factors in this sequence you'd get approximately 9.969

Now there's two questions:

- What is such a sequence called in mathematics (knowing that might enable me to conduct some further googling on my own, without that I'm pretty much lost)?
- Is there a way to calculate the product of all factors of any such sequence without iteration? (the product of factors of the sequence 1..10 is 9.969, the product of factors of the sequence x..y is ...?)