OK so i was playing a RPG earlier today and was astonished at how many people couldn't understand that drop rates are not linear so I decided to create a simple formula as to how to determine %chance to drop after each kill.

I started with this:

(Note)

a: percent to drop

ptd: means percent to drop (the acctual words not the number)

k:kill

(End Note)

ptd 1k:a

ptd 2k:a+(1-a)a= 2a-a^2

ptd 3k:a+(1-a)a+[1-(a+(1-a)a]a

=2a-a^2+[1-2a+a^2)]a

=2a-a^2+a-2a^2+a^3

=3a-3a^2+a^3

ptd 4k:4a-6a^2+4a^3-a^4

ptd 5k:5a-10a^2+10a^3-5a^4+a5

Now i know there's a pattern in there and I'm sure it has something to do with geometric series but I just cant define the pattern.

(I'm sure there's an easier way to do this question than my method and I would love to know it so I could give them a formula real fast but I am also curious as to how to find the pattern in these series)

^^Sorry for bad grammer up there if you didnt understand plz ask me to explain I will be looking back at this every hour or so.