Question

Proving that $\lim\limits_{k\rightarrow\infty}\frac{1}{qk}\log_2\frac{\binom{qk}{k}}{q^{k-1}}=H(\frac{1}{q})-\frac{log_2q}{q}$

score 303 · Answer 1 · 2026-04-16 18:55:49

303

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Proving that $\lim\limits_{k\rightarrow\infty}\frac{1}{qk}\log_2\frac{\binom{qk}{k}}{q^{k-1}}=H(\frac{1}{q})-\frac{log_2q}{q}$

Published on 16 Apr 2026 - 18:55

score 8.6k · Answer 2 · 2026-04-16 22:11:25

8.6k

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Hessian of log-sum-exp $f(z) = \operatorname{log} \sum_{i=1}^n z_i$, find $\nabla^2f(z)$

Published on 16 Apr 2026 - 22:11

score 180 · Answer 3 · 2026-04-16 00:14:36

180

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Showing that $\lim_{x\to 0}\frac{\ln(\sin x+1)}{\sin x} = 1$

Published on 16 Apr 2026 - 0:14

score 418 · Answer 4 · 2026-04-15 22:34:05

418

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find the limit of $\lim\limits_{x\to\infty}(1+x)^{\frac{1}{x}} $

Published on 15 Apr 2026 - 22:34

score 83 · Answer 5 · 2026-04-15 21:34:57

83

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show that $0.5 - \frac{ln(x)}x > 0$

Published on 15 Apr 2026 - 21:34

score 339 · Answer 6 · 2026-04-14 17:03:27

339

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Wolfram Alpha gives different answers for doing the same thing to both sides of this equation.

Published on 14 Apr 2026 - 17:03

score 52 · Answer 7 · 2026-04-09 13:48:46

52

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How can I further simplify this expression?

Published on 09 Apr 2026 - 13:48

score 2.7k · Answer 8 · 2026-04-13 07:13:41

2.7k

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Is swapping numerator and denominator allowed during log base conversion?

Published on 13 Apr 2026 - 7:13

score 1.1k · Answer 9 · 2026-04-19 04:02:44

1.1k

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How can I show that $nlog(n) \neq \Theta(n^2)$?

Published on 19 Apr 2026 - 4:02

score 139 · Answer 10 · 2026-04-14 13:59:17

139

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Limit $\lim_{x \to \infty} \ln x - x$

Published on 14 Apr 2026 - 13:59

score 170 · Answer 11 · 2026-04-11 17:26:03

170

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divergence of a series involving logarithm

Published on 11 Apr 2026 - 17:26

score 119 · Answer 12 · 2026-04-15 18:52:20

119

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If $m=\omega(N log N)$, then what is the order of $N$ in terms of $m$?

Published on 15 Apr 2026 - 18:52

score 234 · Answer 13 · 2026-04-10 19:18:18

234

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Solving equation with 2 variables without bruteforce

Published on 10 Apr 2026 - 19:18

score 1.8k · Answer 14 · 2026-04-16 03:25:38

1.8k

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Solving irrational inequalities: $\sqrt{x^2-7x+10}+9\log_4{x/8}\geq 2x+\sqrt{14x-20-2x^2}-13$

Published on 16 Apr 2026 - 3:25

score 252 · Answer 15 · 2026-04-17 07:48:48

252

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q-analogies of Exponential and Logarithmic functions

Published on 17 Apr 2026 - 7:48

List Question

Proving that $\lim\limits_{k\rightarrow\infty}\frac{1}{qk}\log_2\frac{\binom{qk}{k}}{q^{k-1}}=H(\frac{1}{q})-\frac{log_2q}{q}$

Hessian of log-sum-exp $f(z) = \operatorname{log} \sum_{i=1}^n z_i$, find $\nabla^2f(z)$

Showing that $\lim_{x\to 0}\frac{\ln(\sin x+1)}{\sin x} = 1$

find the limit of $\lim\limits_{x\to\infty}(1+x)^{\frac{1}{x}} $

show that $0.5 - \frac{ln(x)}x > 0$

Wolfram Alpha gives different answers for doing the same thing to both sides of this equation.

How can I further simplify this expression?

Is swapping numerator and denominator allowed during log base conversion?

How can I show that $nlog(n) \neq \Theta(n^2)$?

Limit $\lim_{x \to \infty} \ln x - x$

divergence of a series involving logarithm

If $m=\omega(N log N)$, then what is the order of $N$ in terms of $m$?

Solving equation with 2 variables without bruteforce

Solving irrational inequalities: $\sqrt{x^2-7x+10}+9\log_4{x/8}\geq 2x+\sqrt{14x-20-2x^2}-13$

q-analogies of Exponential and Logarithmic functions

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