Consider this system:
y[n]=y[n-1] + x[n]
It can be verified easily that this system has a finite impulse response (by putting x[n]= delta[n] i.e impulse, and evaluating impulse response h[n]=y[n]). Yet for a unit step input U[n], this system is an unstable system. On wikipedia it is mentioned that FIR filters are always stable
Now my question is , is this an FIR filter or an IIR filter?