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

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

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

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

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

## Comments

Sort by:

TopNewestI don't mean to be a party pooper but there are already plenty of proofs here. – Pi Han Goh · 10 months, 4 weeks ago

Log in to reply

thanks for the link,i only know 2 lol – Hummus A · 10 months, 4 weeks ago

Log in to reply

– Pi Han Goh · 10 months, 4 weeks ago

What are your favorite proofs? Mine is still the classic \(\sin x = x(x\pm \pi)(x\pm 2\pi) \cdots \).Log in to reply

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 – Hummus A · 10 months, 3 weeks ago

Log in to reply

– Ishan Singh · 10 months, 3 weeks ago

\(\sin x = x(x \pm \pi)(x \pm 2\pi) \ldots\) itself requires long a proof.Log in to reply