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# $$\zeta$$!

The main purpose of this note is to gather as many distinct proofs as possible for the below equation

$\large \zeta (2)=1 + \dfrac1{2^2 } + \dfrac1{3^2} + \dfrac1{4^2} + \cdots = \dfrac { { \pi }^{ 2 } }{ 6 }$

Note by Hummus A
9 months, 3 weeks ago

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I don't mean to be a party pooper but there are already plenty of proofs here. · 9 months, 3 weeks ago

oh wow!

thanks for the link,i only know 2 lol · 9 months, 3 weeks ago

What are your favorite proofs? Mine is still the classic $$\sin x = x(x\pm \pi)(x\pm 2\pi) \cdots$$. · 9 months, 2 weeks ago

same!,

i recently saw one that uses $$\frac { 1 }{ { k }^{ 2 } } =\displaystyle\int _{ 0 }^{ 1 }{ \displaystyle\int _{ 0 }^{ 1 }{ (xy)^{ k-1 }dxdy } }$$ and really liked it too · 9 months, 2 weeks ago

$$\sin x = x(x \pm \pi)(x \pm 2\pi) \ldots$$ itself requires long a proof. · 9 months, 2 weeks ago