probability – Show that a random walk on a finite grid graph is recurrent

Good evening, I want to show that a random walk on a graph is recurrent, the graph is a network of nodes which connect together to make a N by M square grid, such as this, my first thought was to somehow get an expression for

$$mathbb{P}[text{on node} n text{after} i text{jumps}]$$,

then express

$$mathbb{P}[text{on node} 0 text{after} i text{jumps}|text{on node} 0 text{at} i=1]$$

then let $$itoinfty$$ and hope it $$=1$$.

Does this sound like the right approach, any pointers?