# Sami Ben Romdhane

less info
reputation
1149139
bio website location age member for 1 year, 10 months seen 20 mins ago profile views 8,374

 94 $\lim_{x \to 1} \frac{x + x^2 + \dots + x^n - n}{x - 1} = \frac{n(n + 1)}{2}$ 62 Prove $\sin^2\theta + \cos^2\theta = 1$ 45 How can I show that $\begin{pmatrix} 1 & 1 \\ 0 & 1\end{pmatrix}^n = \begin{pmatrix} 1 & n \\ 0 & 1\end{pmatrix}$? 31 Prove that $x$ and $x+1$ are coprime numbers 28 Find the tenth derivative of $x^2e^x$

# 97,178 Reputation

 +10 Prove that if $\mathbf A$ is an $n\times m$ matrix, then $\text{tr}(\mathbf A \mathbf A')=\text{tr}(\mathbf A' \mathbf A)$ +10 Show that $\lim_{n\to\infty}\sum_{k=1}^n\bigl|k\bigl(f\bigl(\frac{1}{k}\bigr)-f\bigl(-\frac{1}{k}\bigr)\bigr)-2f'(0)\bigr|$ exists -2 Show that $\mathbb{Z}[\sqrt{5}]$ is not a UFD +10 Multiple choice question about limits and continuity? (Or, $\tan x$ is continuous?!)

# 12 Questions

 18 Order of matrices in $GL_2(\mathbb{Z})$ 17 The series $\sum_{n=1}^{+\infty}\frac{1}{1^2+2^2+\cdots+n^2}.$ 17 Functions $f$ satisfying $f\circ f(x)=2f(x)-x,\forall x\in\mathbb{R}$. 12 Prove the inequality: $\prod_{j=1}^ka_{jj}\leq\left(\frac{1}{k}\sum_{j=1}^k\lambda_j\right)^k.$ 7 Limit of a sequence with indeterminate form

# 265 Tags

 2k calculus × 641 748 integration × 221 2k linear-algebra × 581 735 matrices × 227 1k real-analysis × 421 517 algebra-precalculus × 135 1k sequences-and-series × 411 452 convergence × 151 1k limits × 352 397 analysis × 140

# 9 Accounts

 Mathematics 97,178 rep 1149139 Area 51 151 rep 2 Stack Overflow 101 rep 1 TeX - LaTeX 101 rep 1 Ask Ubuntu 101 rep