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 34 Zero to the zero power - is $0^0=1$? 20 Funny identities 17 Proving the identity $\sum_{k=1}^n {k^3} = \big(\sum_{k=1}^n k\big)^2$ without induction 9 The contributions of James Sylvester to linear algebra. 7 Computing the Gaussian integral with Fourier methods?

### Reputation (1,224)

 +10 Proving the identity $\sum_{k=1}^n {k^3} = \big(\sum_{k=1}^n k\big)^2$ without induction +20 Proving the identity $\sum_{k=1}^n {k^3} = \big(\sum_{k=1}^n k\big)^2$ without induction +10 Proof of $\int_0^\infty \left(\frac{\sin x}{x}\right)^2 \mathrm dx=\frac{\pi}{2}.$ +10 Zero to the zero power - is $0^0=1$?

### Questions (8)

 16 Consecutive birthdays probability 2 Is $\det$ of $M_{i,j} = \min(x_i, x_j)^2 \left( 3 \max(x_i, x_j) - \min(x_i, x_j) \right)$ non zero? 2 Inequality based on the minimum of a function 1 Linear least squares with non-negativity constraint 1 Solutions of $\frac{1- x^{\alpha}}{1- x^{\beta}} = \gamma$

### Tags (37)

 55 algebra-precalculus × 3 23 sequences-and-series × 3 34 real-analysis × 2 21 summation × 2 34 discrete-mathematics 21 visualization × 2 34 exponentiation 14 integration × 2 34 faq 11 linear-algebra × 5

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