impulse response of a causal LTI system
HINT:
Just write down the values of the output signal $y[n]$ for $x[n]=\delta[n]$ for values of $n$ from $0$ to $N-1$ (you don't need any specific value for $N$, just use $n=0,1,2,\ldots$ and then you'll see what happens at $n=N-1$). Then figure out what happens at $n=N$, and what consequences this has on the output values for $n&gt;N$. You may be surprised to find out that the given system has a finite length impulse response, even though it is recursive.