Infinite Sum of 1/n^2 : Complex Fourier Series

In this video, I destroy the Basel problem with Complex Fourier Series instead of the Classical Fourier Series.
Featuring Complex Parseval's Theorem.
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#Calculus #FourierSeries #ComplexFourierSeries #Integration #DefiniteIntegral #Pi #Periodic #Complex #InfiniteSeries #InfiniteSum #Exponential #Sine #Cosine #Trigonometry #Imaginary #Real #Coefficient #ParsevalTheorem #Modulus #i #Mathematics #Math #Sumof1/n^2
#Even #Convergence #Divergence #Odd
#DrPeyam #BlackPenRedPen #FlammableMaths #AndrewDotson #3Blue1Brown #MichalePenn #VibingMaths #Tibees #SteveMould

[@williammartin4416]

What justifies being able to ignore Cn for n=0 simply because it diverges?

[@GammaDigamma]

If you try to calculate c_0 explicitly, you indeed get zero. I believe I miswrote the Fourier series expansion when I summed from -infinity to infinity; since c_0 is zero, the expansion is actually from -infinity to -1 and from 1 to infinity.
Sorry for the lazy arguments, this is an older video.