Zeta?

Calculus Level 3

∑ n = 1 ∞ 1 n 2 = ? \large \displaystyle \sum _{ n=1 }^{ \infty }{ \frac { 1 }{ { n }^{ 2 } } } = \, ?

Submit your answer to 2 decimal places.


The answer is 1.64.

Mehul Arora by Mehul Arora , 20, India

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2 solutions

Rishabh Jain
Feb 15, 2016

∑ n = 1 ∞ 1 n 2 = π 2 6 ≈ 1.64 \huge\sum _{ n=1 }^{ \infty } \frac { 1 }{ { n }^{ 2 } } =\dfrac{\pi^2}{6}\approx\boxed{\color{#007fff}{1.64}} This is a famous problem.... See this for further analysis of this problem..

3 Helpful 0 Interesting 0 Brilliant 0 Confused

@Mehul Arora [Duplicate Problem](https://brilliant.org/discussions/thread/proof-that-zeta2dfracpi26/)

: 3 \large\boxed{:3}

Aditya Kumar - 5 years, 3 months ago

Did the same

Aditya Kumar - 5 years, 1 month ago

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Yet again.... ⌣ ¨ \ddot\smile

Rishabh Jain - 5 years, 1 month ago
Mateus Gomes
Feb 15, 2016

∑ n = 1 ∞ 1 n 2 = π 2 6 \sum_{n=1}^{\infty}\frac{1}{n^2}=\frac{\pi^2}{6}

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Can you explain how you got this?

Aditya Kumar - 5 years, 4 months ago

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