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### Complex Analysis Solution to the Basel Problem ($\sum_{k=1}^\infty \frac{1}{k^2}$) [duplicate]

Most of us are aware of the famous "Basel Problem": $$\sum_{k=1}^\infty \frac{1}{k^2} = \frac{\pi^2}{6}$$ I remember reading an elegant proof for this using complex numbers to help find the value of ...
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### Showing $\sum _{k=1} 1/k^2 = \pi^2/6$ [duplicate]

Possible Duplicate: Different methods to compute $\sum\limits_{n=1}^\infty \frac{1}{n^2}$ Does $\sum\limits_{k=1}^n 1 / k ^ 2$ converge when $n\rightarrow\infty$? I read my book of EDP, and ...
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### Sum of $\frac{1}{n^{2}}$ for $n = 1 ,2 ,3, ...$? [duplicate]

Possible Duplicate: Different methods to compute $\sum_{n=1}^\infty \frac{1}{n^2}$. I just got the "New and Revised" edition of "Mathematics: The New Golden Age", by Keith Devlin. On p. 64 it ...
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### Proving $\int_0^1\frac{\log (1-x)}{x}\mathrm dx=-\frac{\pi^2}6$ [duplicate]

It is a well known fact that $\displaystyle\sum_{k=1}^{\infty}\frac1{k^2}=\frac{\pi^2}6$. I wanted to prove this using elementary techniques. By doing some easy algebra, I found it was sufficient to ...
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### Simpler derivation of $\sum_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2}{6}$ [duplicate]

I know that the equality $$\sum_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2}{6}$$ can be proved in numerous ways by using the Fourier series. However, is there a way to derive it using more fundamental ...
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### How to calculate $S_{n}=\sum_{i=1}^{n}\frac{1}{i^{2}}$ [duplicate]

In math lesson, my teacher told me that Euler once used a very delicate method to calculate $\displaystyle S_{n}=\sum_{i=1}^{n}\frac{1}{i^{2}}$ and wrote a paper about it. I wonder how to calculate ...
### Show that $\sum_{n=1}^{\infty}{\frac{1}{n^2}}=\frac{\pi^2}{6}$ [duplicate]
Show that $$\sum_{n=1}^{\infty}{\frac{1}{n^2}}=\frac{\pi^2}{6}$$ Anyone can help ?