Is there a way to express this equation where you have an integer $x$ and an integer $n$ and you do:
$$ x^n + x^{n-1} + x^{n-2} + ... + x^{n-n} $$
Is there a name for this type of equation and how can I write it more succinctly? I haven't done math in so long and don't even know how to search for this
On
It is called geometric series. In your case, you can verify that
$$\frac{1-x^{n+1}}{1-x}$$ Is the quantity you are looking for, except if $x=1$. If $x=1$ then you can deduce what is the result.
There's a very simple way, but in reverse order.
$$ \sum_{i=0}^n x^i $$
As a short explanation: $\sum$ is used to indicate summation.
Each value, starting at the one indicated below the symbol ( $0$ in this case) and then incremented by one until you reach the value above the symbol ( $n$ in this case) is used as indicated in the right hand expression (exponential in this case) and summed up with each increment.