The joy of multisection: elementary approaches to Ramanujan's lacunary identities for Bernoulli numbers

An identity by Ramanujan related to the multisection of Bernoulli numbers is revisited. Two alternative approaches are proposed, both relying on the multisection technique. A geometric approach reveals the role played by the symmetries of the summation domain in the complex plane induced by the multisection technique. The second approach, based on generating functions, allows us to extend Ramanujan’s identity to other special functions such as Eisenstein’s series.