List questions from logarithms

Published on 25 Mar 2026 - 19:05

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Let $k\in\Bbb{N}$. Prove that $0<\frac{1}{k}-\ln(1+\frac{1}{k})<\frac{1}{2k^2}$

Published on 19 Nov 2018 - 21:58

667

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Why does $\int_1^\sqrt2 \frac{1}{x}\ln\left(\frac{2-2x^2+x^4}{2x-2x^2+x^3}\right)dx$ equal to $0$?

Published on 25 Mar 2026 - 7:44

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Prove $π(x+y)- π(x) \ll \frac y{\log (\log (y))}$ using Legendre sieve such that $10 ≤ y ≤ x$

Published on 25 Mar 2026 - 6:13

75

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Integrate $\int_{-\infty}^\infty [4(\log r_1 - \log r_2) - 2(x_1^2/r_1^2 - x_2^2/r_2^2)]^2 dx$

Published on 25 Mar 2026 - 1:18

1.1k

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Proof that $H(X) \leq \log(|A|)$ (Shannon entropy)

Published on 25 Mar 2026 - 12:54

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Simple inequality with natural logarithm

Published on 21 Nov 2018 - 19:37

61

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What is the value of following limit?

Published on 23 Nov 2018 - 6:20

101

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Is $1 + \frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{x} < \log_2 x$

Published on 25 Mar 2026 - 6:04

40

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numerical analysis and weakness of calculator

Published on 25 Mar 2026 - 22:23

41

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Solving sets of 3 equations with 3 unknown with some logarithms thrown in.

Published on 23 Nov 2018 - 12:51

58

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Exponential Approximation

Published on 26 Mar 2026 - 6:17

50

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Finding the limit of $\frac{x}{e^x}$ from the graph of reciprocal function

Published on 28 Mar 2026 - 21:44

467

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Why are we using "Euler's Number" constantly?

Published on 26 Mar 2026 - 9:45

636

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Prove that $\mathrm{arcsinh}(x)$ is an odd function

Published on 25 Mar 2026 - 11:08

List Question

Inequality in proof of 2nd Borel-Cantelli Lemma

Let $k\in\Bbb{N}$. Prove that $0<\frac{1}{k}-\ln(1+\frac{1}{k})<\frac{1}{2k^2}$

Why does $\int_1^\sqrt2 \frac{1}{x}\ln\left(\frac{2-2x^2+x^4}{2x-2x^2+x^3}\right)dx$ equal to $0$?

Prove $π(x+y)- π(x) \ll \frac y{\log (\log (y))}$ using Legendre sieve such that $10 ≤ y ≤ x$

Integrate $\int_{-\infty}^\infty [4(\log r_1 - \log r_2) - 2(x_1^2/r_1^2 - x_2^2/r_2^2)]^2 dx$

Proof that $H(X) \leq \log(|A|)$ (Shannon entropy)

Simple inequality with natural logarithm

What is the value of following limit?

Is $1 + \frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{x} < \log_2 x$

numerical analysis and weakness of calculator

Solving sets of 3 equations with 3 unknown with some logarithms thrown in.

Exponential Approximation

Finding the limit of $\frac{x}{e^x}$ from the graph of reciprocal function

Why are we using "Euler's Number" constantly?

Prove that $\mathrm{arcsinh}(x)$ is an odd function

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