Henricus Heads Home, A note on simple symmetric random walks

Corrections:

None yet, let me know if you spot any mistake!

Acknowledgements:

This proof is almost entirely based on the discussion presented in chapter three of William Feller's An Introduction to Probability Theory and Its Applications, Vol. 1. I have attempted to make the text more accessible by expanding the arguments presented there.

I learnt this as part of a Ramanujan club project with the guidance of Dr. Kartick Adhikari.