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Sami Ben Romdhane
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 112 How to show $\lim_{x \to 1} \frac{x + x^2 + \dots + x^n - n}{x - 1} = \frac{n(n + 1)}{2}$? 70 Prove $\sin^2\theta + \cos^2\theta = 1$ 49 How can I show that $\begin{pmatrix} 1 & 1 \\ 0 & 1\end{pmatrix}^n = \begin{pmatrix} 1 & n \\ 0 & 1\end{pmatrix}$? 33 Prove that $x$ and $x+1$ are coprime numbers 30 Find the tenth derivative of $x^2e^x$

### Reputation (1)

 +10 How to prove that $\sum_{k=0}^n\cos(k\pi)\binom{n}{k}=0$? +10 How to show $\int_{0}^\infty e^{x^2}dx$ does not converge? +10 Can a positive function defined on a closed interval have $0$ as an inf? +10 Definition of abs() function

### Questions (12)

 20 The series $\sum_{n=1}^{+\infty}\frac{1}{1^2+2^2+\cdots+n^2}.$ 20 Order of matrices in $GL_2(\mathbb{Z})$ 19 Functions $f$ satisfying $f\circ f(x)=2f(x)-x,\forall x\in\mathbb{R}$. 14 Prove the inequality: $\prod_{j=1}^ka_{jj}\leq\left(\frac{1}{k}\sum_{j=1}^k\lambda_j\right)^k.$ 10 Limit of a sequence with indeterminate form

### Tags (269)

 2k calculus × 691 848 matrices × 257 2k linear-algebra × 652 804 integration × 233 2k real-analysis × 453 557 algebra-precalculus × 141 2k sequences-and-series × 459 494 convergence × 163 1k limits × 382 430 analysis × 148

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 Area 51 151 rep 2 Stack Overflow 101 rep 1 TeX - LaTeX 101 rep 1 Ask Ubuntu 101 rep English Language & Usage 101 rep 1