# David Čepelík

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bio website location Prague, Czech Republic age 21 member for 1 year, 1 month seen Jan 29 at 13:26 profile views 110

Mathematics student at the Faculty of Mathematics and Physics, Charles University in Prague.

# 16 Questions

 26 $\lim_{x \to 1} \frac{x + x^2 + \dots + x^n - n}{x - 1} = \frac{n(n + 1)}{2}$ 8 Evaluating the limit of a sequence given by recurrence relation $a_1=\sqrt2$, $a_{n+1}=\sqrt{2+a_n}$. Is my solution correct? 8 What is the fastest way to find the characteristic polynomial of a matrix? 8 Are there more planar graphs on $5n$ vertices than bipartite graphs on $n$ vertices? 6 Convergence of $\sum_n^\infty (-1)^n\frac{\sin^2 n}n$

# 736 Reputation

 +2 How to prove: If $a \to -\infty$ and $b$ is bounded from below by a constant $k\in\Bbb R^{>0}$, then the $a\cdot b\to -\infty$ +110 How to test whether I am suitable to pursue mathematics? +10 Prove the following inequality using induction: $(1 + \epsilon)^n \leq 1+ (2^n - 1)\epsilon$ for every $n \geq 1$ and $0 \leq \epsilon \leq 1$ +5 $\lim_{x \to 1} \frac{x + x^2 + \dots + x^n - n}{x - 1} = \frac{n(n + 1)}{2}$

 11 How to test whether I am suitable to pursue mathematics? 2 Prove that $\lim_{n \to\infty} \frac{x_{n+1}}{x_n} = a \implies \lim_{n \to\infty} \sqrt[n]{x_n} = a$. 2 Gaps between primes 1 Prove the following inequality using induction: $(1 + \epsilon)^n \leq 1+ (2^n - 1)\epsilon$ for every $n \geq 1$ and $0 \leq \epsilon \leq 1$ 1 Proving Limit False

# 38 Tags

 11 advice 2 proof-verification × 2 11 soft-question 2 prime-numbers 3 sequences-and-series × 10 2 number-theory 2 inequality × 3 1 limits × 5 2 limit-theorems × 2 1 functional-inequalities

# 5 Accounts

 Mathematics 736 rep 213 Stack Overflow 270 rep 28 Electrical Engineering 148 rep 3 English Language & Usage 123 rep 4 MathOverflow 101 rep