David Čepelík
Reputation
1,142
Next privilege 2,000 Rep.
7 21
Impact
~24k people reached

### Questions (25)

 43 How to show $\lim_{x \to 1} \frac{x + x^2 + \dots + x^n - n}{x - 1} = \frac{n(n + 1)}{2}$? 14 What is the fastest way to find the characteristic polynomial of a matrix? 13 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 Are there more planar graphs on $5n$ vertices than bipartite graphs on $n$ vertices? 6 Convergence of $\sum_n^\infty (-1)^n\frac{\sin^2 n}n$

### Reputation (1,142)

 +10 What is the fastest way to find the characteristic polynomial of a matrix? +10 Can a curve be an asymptote? +10 Derivatives of multivariable functions +10 Gaps between primes

 14 How to test whether I am suitable to pursue mathematics? 5 Gaps between primes 2 Prove that $\lim_{n \to\infty} \frac{x_{n+1}}{x_n} = a \implies \lim_{n \to\infty} \sqrt[n]{x_n} = a$. 1 Length of the Union of Intervals is less than the Sum of Each Length of Intervals? 1 Probability doubles if you switch cards when the third card is revealed, How?

### Tags (46)

 14 advice 3 sequences-and-series × 11 14 soft-question 2 limits × 5 5 number-theory 2 inequality × 3 5 prime-gaps 2 proof-verification × 3 5 prime-numbers 2 probability-limit-theorem × 2

### Accounts (14)

 Mathematics 1,142 rep 721 Stack Overflow 443 rep 314 Server Fault 197 rep 311 Electrical Engineering 170 rep 6 Code Review 168 rep 7