How to express a formula that iterates over itself n number of times? I'm not very good at math so I might use the wrong words when searching for an answer (i even don't know what tags to apply).
I have an expression in a loop and the only way I can explain it is something like this.
x = h
Loop n times
  x = k*x
end loop
Result = x

h is the initial value of x. For each loop x = k*x
n is the number of loops
After n loops x now hold the result.
How do I express this mathematically?
 A: First of all: there are no problems in "not being good at math". If you want a math solution, them you're free to come at SE and ask.
For your question, we can start by $x_0 = h$.
Then, we define $f(x)$ (or $f\circ x$) as whatever is in the loop: $f\circ x = k\cdot x$.
As the result is the end of the iteration of the loop (with start at $x_0$), we can use the recomposition¹ notation. Letting $y$ be your result:
$$
y = \underbrace{f(f(\cdots f(x_0)\cdots ))}_{n \textrm{ times } f(\textrm{ something })}
= \underbrace{f\circ f\circ\cdots f\circ x_0}_{n \textrm{ times } f\,\circ\textrm{ something}}
= f\overset n\circ (x_0)
$$
But for your case, in specific, as $f\circ x = kx$, we have
$$
y = f\overset n\circ (x_0)
= (kx)\overset n\circ (x_0)
= (k^n x)\circ(x_0)
= k^n x_0
$$
Note:

*

*Recomposing is composing again

*Some prefer notating $f^{\circ n} x$

*f \overset{n}\circ x evaluates to $f \overset{n}\circ x$
A: Initially, $x=h$. After one iteration, $x'=kx=kh$. After two iterations, $x''=kx'=kkh=k^2h$. More generally, after $n$ iterations,
$$x^{(n)}=k^nh.$$

In a more mathematical language, you have the recurrent sequence defined by
$$x_0=h,\\x_n=kx_{n-1}.$$
