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Without differentiation or integration, or number theory, could we still prove this infinite sum? | Visit to get started learning STEM for free, and the first 200 people will get 20% off their annual premium subscription. π/4 = 1 - 1/3 1/5 -..., also called the Leibniz series, is quite famous, but the usual proof involves differentiation or integration. The more visual geometric proof still relies a lot on some advanced theorems from number theory, but given how simple the series is, is it possible to have an even simpler proof? Yes! And this video tries to explain this. Actually, similar to the previous proof, this proof has been at the video ideas list for quite a long time - so it's good to finally see this out! By the way, on second thought, this looks similar to Fourier coefficients, at least the time average bit - though I can't see whether this is the same proof as the one using Fourier series of sgn(x). It feels very connect
