How does
$X_{n+1} = (1-10000h)X_n$
become
$X_n= (1-10000h)^{n+1}$
I can't seem to understand the solution to one of my questions because of this transformation of $X_{n+1}$. I'm not sure how the $X_n$ vanishes.
How does
$X_{n+1} = (1-10000h)X_n$
become
$X_n= (1-10000h)^{n+1}$
I can't seem to understand the solution to one of my questions because of this transformation of $X_{n+1}$. I'm not sure how the $X_n$ vanishes.
It should be $X_n=(1-10000h)^nX_0$.
From $X_{n+1}=(1-10000h)X_n$, letting $n=0$, you get $X_1=(1-10000h)X_0$. Then, letting $n=1$, you get $X_2=(1-10000h)X_1=(1-10000h)^2X_0$. Then, letting $n=2$, you get $X_3=(1-10000h)X_2=(1-10000h)^3X_0$. With any luck, by now you see the pattern, and then you can prove it by induction on $n$.