Waste less time on Facebook — follow Brilliant.
×

\(\zeta\)!

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
8 months, 1 week ago

No vote yet
1 vote

Comments

Sort by:

Top Newest

I don't mean to be a party pooper but there are already plenty of proofs here. Pi Han Goh · 8 months, 1 week ago

Log in to reply

@Pi Han Goh oh wow!

thanks for the link,i only know 2 lol Hummus A · 8 months, 1 week ago

Log in to reply

@Hummus A What are your favorite proofs? Mine is still the classic \(\sin x = x(x\pm \pi)(x\pm 2\pi) \cdots \). Pi Han Goh · 8 months, 1 week ago

Log in to reply

@Pi Han Goh 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 Hummus A · 8 months, 1 week ago

Log in to reply

@Pi Han Goh \(\sin x = x(x \pm \pi)(x \pm 2\pi) \ldots\) itself requires long a proof. Ishan Singh · 8 months, 1 week ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...