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Sami Ben Romdhane
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 106 How to show $\lim_{x \to 1} \frac{x + x^2 + \dots + x^n - n}{x - 1} = \frac{n(n + 1)}{2}$? 68 Prove $\sin^2\theta + \cos^2\theta = 1$ 49 How can I show that $\begin{pmatrix} 1 & 1 \\ 0 & 1\end{pmatrix}^n = \begin{pmatrix} 1 & n \\ 0 & 1\end{pmatrix}$? 32 Prove that $x$ and $x+1$ are coprime numbers 30 Find the tenth derivative of $x^2e^x$

### Reputation (1)

 +25 Prove that if $v_1,v_2,…,v_r$ form a linearly independent set of vectors in $V$… +10 Find the tenth derivative of $x^2e^x$ +10 Find a formula for $\sum\limits_{k=1}^n \lfloor \sqrt{k} \rfloor$ +10 Every bounded monotone sequence converges

### 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 $f\circ f(x)=2f(x)-x,\forall x\in\mathbb{R}$. 13 Prove the inequality: $\prod_{j=1}^ka_{jj}\leq\left(\frac{1}{k}\sum_{j=1}^k\lambda_j\right)^k.$ 9 Limit of a sequence with indeterminate form

### Tags (271)

 2k calculus × 695 842 matrices × 258 2k linear-algebra × 652 801 integration × 232 1k real-analysis × 454 551 algebra-precalculus × 141 1k sequences-and-series × 459 498 convergence × 164 1k limits × 383 432 analysis × 149

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