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 8 Compute $\lim_{N\to \infty} A_N$ where $\{A_N\}$ is a sequence of matrices 5 Inverse of Strictly Monotone Function 4 Range of $\frac{\cos\theta_1+\cdots+\cos\theta_{10}}{\sin\theta_1+\cdots+\sin\theta_{10}}$ given $\sin^2\theta_1+\cdots+\sin^2\theta_{10}=1$ 4 Proving that $2^{2018}-2^{2016}+2^{2013}$ is divisible by $5$. 4 For which $x,y, z$ we have $390=x^3+y^3+z^3$ with $x, y, z$ integers?

### Reputation (1,634)

 +10 Make $2^8 + 2^{11} + 2^n$ a perfect square +20 Complement of a Disconnected Graph is Connected +10 Inequality $a^2b(a-b) + b^2c(b-c) + c^2a(c-a) \geq 0$ +10 Inequality $\dfrac{1}{\sqrt{1+2x}} + \dfrac{1}{\sqrt{1+2y}} + \dfrac{1}{\sqrt{1+2z}} \leq \sqrt{3}$.

### Questions (33)

 9 Showing $64$ divides $5^n-8n^2+4n-1$ without induction 7 Is $x=2,y=13$ the unique solution? 5 Alternative approaches to prove the following inequality 5 Solving the equation $f(x)=f^{-1}(x)$. [duplicate] 4 Sum to infinity of a Series

### Tags (67)

 21 inequality × 23 8 matrices 16 algebra-precalculus × 15 8 matrix-calculus 12 a.m.-g.m.-inequality × 12 8 limits 8 cauchy-schwarz-inequality × 6 5 contest-math × 14 8 linear-algebra × 3 5 calculus × 6

### Bookmarks (31)

 28 Why should the substitution be injective when integrating by substitution? 27 Proving $abcd+3\geq a+b+c+d$ 26 How to prove this inequality $x^2_{n}\le\frac{8}{3}$ 12 Show that given a set of positive n integers, there exists a non-empty subset whose sum is divisible by n 9 general formula for the nth derivative of $f(x)=\frac{1}{1+e^{x}}$

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