Question

suppose a container contains 5 units of liquid from which two units are taken out and replaced by water after two operations the quantity of pure liquid =
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Answer 1

Answer:

Suppose a container contains x of liquid from which y units are taken out and replaced by water.After n operations, the quantity of pure liquid is: x(1−

y

x

)n I understand the concept but I am unable to derive it. I tried by taking 10 litre of liquid and adding 2 litre water for 2 operations 10:0

operation 1: 10−2:2

operation 2:

quantity of liquid removed=

2∗8

10

finally 8−

8

5

:2+2−

2

5

which is same as the formula but I am not able to prove 10(1−

2

10

)2 from it. I need a general proof of (x(1−y/x)n).