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### Questions (37)

 8 Find $\sum_{n=1}^{\infty}\tan^{-1}\frac{2}{n^2}$ 8 Soft Question: Suggestions on mathematics resources for problem solving. 7 Find $\lim\limits_{x\to0^+}x(\lfloor \frac{1}{x}\rfloor+\lfloor \frac{2}{x}\rfloor+\cdots+\lfloor \frac{k}{x}\rfloor), \, k \in \mathbb N$. 5 Proving a lower bound on the limit superior of a sequence. 4 Let $A=\begin{bmatrix} 1 & 2\\ 3& 4 \end{bmatrix}$ then det$(A^3-6A^2+5A+3I)=3$

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 3 Sum of all the numbers in the grid. 2 How old did the man live to be? 1 Suppose $x, y, z$ are positive real number such that $x + 2y + 3z = 1$. Find the maximum value of $xyz^2$ 1 How can I show that an odd degreed polynomial with coefficients in the real space always has a root in $\mathbb{R}$? 0 Let $G$ be a group of all $2 \times 2$ matrices over $Z_p$ with determinant $1$ under matrix multiplication. To find the order of $G$.

### Tags (78)

 5 algebra-precalculus × 2 1 maxima-minima 3 summation × 6 0 sequences-and-series × 10 3 arithmetic-progressions 0 matrices × 8 1 real-analysis × 11 0 abstract-algebra × 7 1 linear-algebra × 11 0 limits × 7

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