I need to receive 1 apple. When I buy 1 apple I always return 0.2% of apples back.
I.e. if I buy 1 apple then I receive 0.998 of apple.
If I buy 1.002 I receive 0.999996 of apple
If I buy 1.002004008016032064128256... then I receive 1 apple.
How to calculate the amount of apples I need to buy so that when I return 0.2% of it I would have 1 apple? Which formula I need to use?
Let's say, that you buy $x$ units of something (e.g. apples).
You have to return $0.2\%$ of what you've bought, so after that you have $(1-0.002)x$ units of something.
Now you want, that after returning $0.2\%$ you would have $n$ apples.
Thus: $$(1-0.002)x=n$$
You just need to solve this equation for $x$: $$x=\frac{n}{.998}$$