Christmas Bunny
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### Questions (97)

 25 Does there exist a sequence $\{a_n\}_{n\ge1}$ with $a_n < a_{n+1}+a_{n^2}$ such that $\sum_{n=1}^{\infty}a_n$ converges? 13 Showing that $|\cos x|+|\cos 2x|+\cdots+|\cos 2^nx|\geq \dfrac{n}{2\sqrt{2}}$ 11 Prove that there exists $t$ such that $0\le t\le T$ and $\int_0^Te^{-x}y'y''\,dx=\int_0^ty'y''\,dx$. 11 Find the maximum and minimum of $\sum_{i=1}^{n-1}x_ix_{i+1}$ subject to $\sum_{i=1}^nx_i^2=1$. 11 Prove that $\int_0^1|f''(x)|dx\ge4.$

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 3 Proving $n^q$ is algebraic when $n\in \mathbb N$ and $q\in \mathbb Q$. 3 Finding the index such that all partial sums are nonnegative 1 Find the maximum and minimum of $\sum_{i=1}^{n-1}x_ix_{i+1}$ subject to $\sum_{i=1}^nx_i^2=1$. 0 $\sum_{i=1}^nx_i^2+2\sum_{1\le k 3j$, there exists positive integers $s,t$ such that $k > |\sqrt{s}-\sqrt{t}| > j$

### Tags (88)

 4 contest-math × 57 1 analysis × 55 3 real-analysis × 65 1 optimization × 5 3 algorithms × 4 0 inequality × 28 3 integer-programming × 2 0 calculus × 20 3 algebraic-number-theory 0 integration × 17

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 Mathematics 2,087 rep 521 Chinese Language 155 rep 5 Stack Overflow 120 rep 6 Programming Puzzles & Code Golf 101 rep 1 Theoretical Computer Science 101 rep 1