There is a formula in my book for questions of type,
A vessel contains $x$ amount of milk out of which $y$ amount is taken out and replaced with water. After $n$ such operations what will be the amount of Milk?
The formula says remaining Milk after $n$ such operations = $x\left(1-\dfrac yx\right)^n$
- How can we prove this formula?
I actually somehow proved this a long time ago with the principle of mathematical induction but can't recall the second step. For $n=0$ and $n=1$ the formula is obviously true. Then we can assume that for a specific $n$ the formula holds. But I do not remember how to show the validity of formula for $(n+1)$th operation.
If there are other proofs than Induction then I would like know them. Thanks.
I solved this problem for someother OP. Here you go!