The r-generalized Fibonacci numbers (r\(\geq 2)\) are defined by \(u_{r,n}=0\) for \(n<0\), \(u_{r,0}=1\) and \(u_{r,n}=\sum^{r}_{i=1}u_{r,n-i}\) for \(n>0\). The main result of the paper shows the convergence of the sequence \(u_{r,n}/u_{r,n-1},\) which is a known result but its present proof is a new one. Geometrical and electrical interpretation of the r-generalized Fibonacci numbers are also given.