Question

Prove that $(1+1/a)^{a+1}<(1+1/b)^{b+1}$ if $a>b>0$

score 77 · Answer 1 · 2017-06-02 09:12:01

77

Views

Prove that $(1+1/a)^{a+1}<(1+1/b)^{b+1}$ if $a>b>0$

Published on 02 Jun 2017 - 9:12

score 173 · Answer 2 · 2017-06-03 02:07:36

173

Views

Is this sum $\sum_{k=1}^{\infty}\left({1\over kx}+{1\over kx-1}+{1\over kx-2}+\cdots+{1\over kx-x+1}-\ln{k+1\over k}\right)=\gamma+\ln{x}$ correct?

Published on 03 Jun 2017 - 2:07

score 27 · Answer 3 · 2017-06-04 07:36:51

27

Views

Question about De Moivre's method and e

Published on 04 Jun 2017 - 7:36

score 2k · Answer 4 · 2017-06-04 20:58:24

2k

Views

If some series of n terms is deranged, what is the probability that no term stands next to a term it was next to originally?

Published on 04 Jun 2017 - 20:58

score 378 · Answer 5 · 2017-06-05 13:32:33

378

Views

How can we show that $\sum_{n=1}^{\infty}\left({x\over n}-\ln{n+x\over n}\right)=x\gamma+\ln(x!)?$

Published on 05 Jun 2017 - 13:32

score 2.9k · Answer 6 · 2017-06-10 07:35:31

2.9k

Views

Looking for the 100 first decimal digits of $e$ (mathematical constant)

Published on 10 Jun 2017 - 7:35

score 166 · Answer 7 · 2017-06-26 18:24:26

166

Views

How do I find $x$ if I know $y$

Published on 26 Jun 2017 - 18:24

score 5.1k · Answer 8 · 2017-07-02 14:18:25

5.1k

Views

Duhamel's formula, variation of constants formula, easy differentiation of the right hand side

Published on 02 Jul 2017 - 14:18

score 123 · Answer 9 · 2017-07-13 06:18:54

123

Views

Integral form of Euler's constant

Published on 13 Jul 2017 - 6:18

score 143 · Answer 10 · 2017-07-26 15:16:08

143

Views

Something strange regarding Euler's Identity

Published on 26 Jul 2017 - 15:16

score 104 · Answer 11 · 2017-08-02 16:55:45

104

Views

The Sum of $\frac 1{n+k}$ and $1+\frac 2{(3k)^3-3k}$

Published on 02 Aug 2017 - 16:55

score 38 · Answer 12 · 2017-09-02 19:36:21

38

Views

Connection between fractional derivatives and the Eulers constant

Published on 02 Sep 2017 - 19:36

score 493 · Answer 13 · 2017-09-04 02:21:47

493

Views

Why does $(\sum_{i=1}^x \frac{1}{i}) - \ln(x+\frac{1}{2})$ converge to $\gamma$ a lot faster than $(\sum_{i=1}^x \frac{1}{i}) - \ln(x)$

Published on 04 Sep 2017 - 2:21

score 109 · Answer 14 · 2017-09-05 06:34:43

109

Views

Why does $\sum_{i=1}^x \frac xi - \lfloor \frac xi \rceil \approx 0.03648x$ instead of $x(1-2\gamma)$

Published on 05 Sep 2017 - 6:34

score 89 · Answer 15 · 2017-09-09 19:10:23

89

Views

How can we show that $3\gamma=\lim_{x\to \infty}\left(xe^{1\over x}-e^{-{1\over x}}\Gamma\left({1\over x}\right)\right)?$

Published on 09 Sep 2017 - 19:10

List Question

Prove that $(1+1/a)^{a+1}<(1+1/b)^{b+1}$ if $a>b>0$

Is this sum $\sum_{k=1}^{\infty}\left({1\over kx}+{1\over kx-1}+{1\over kx-2}+\cdots+{1\over kx-x+1}-\ln{k+1\over k}\right)=\gamma+\ln{x}$ correct?

Question about De Moivre's method and e

If some series of n terms is deranged, what is the probability that no term stands next to a term it was next to originally?

How can we show that $\sum_{n=1}^{\infty}\left({x\over n}-\ln{n+x\over n}\right)=x\gamma+\ln(x!)?$

Looking for the 100 first decimal digits of $e$ (mathematical constant)

How do I find $x$ if I know $y$

Duhamel's formula, variation of constants formula, easy differentiation of the right hand side

Integral form of Euler's constant

Something strange regarding Euler's Identity

The Sum of $\frac 1{n+k}$ and $1+\frac 2{(3k)^3-3k}$

Connection between fractional derivatives and the Eulers constant

Why does $(\sum_{i=1}^x \frac{1}{i}) - \ln(x+\frac{1}{2})$ converge to $\gamma$ a lot faster than $(\sum_{i=1}^x \frac{1}{i}) - \ln(x)$

Why does $\sum_{i=1}^x \frac xi - \lfloor \frac xi \rceil \approx 0.03648x$ instead of $x(1-2\gamma)$

How can we show that $3\gamma=\lim_{x\to \infty}\left(xe^{1\over x}-e^{-{1\over x}}\Gamma\left({1\over x}\right)\right)?$

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