Question

Why is $(e^{2πi})^i$ different from $(e^i)^{2πi}$

score 45 · Answer 1 · 2020-10-09 13:33:31

45

Views

Why is $(e^{2πi})^i$ different from $(e^i)^{2πi}$

Published on 09 Oct 2020 - 13:33

score 420 · Answer 2 · 2020-10-15 13:09:19

420

Views

Strange similar approximations of pi and e

Published on 15 Oct 2020 - 13:09

score 45 · Answer 3 · 2020-10-20 07:55:56

45

Views

Using the number e to find the limit of a sequence

Published on 20 Oct 2020 - 7:55

score 171 · Answer 4 · 2020-10-25 10:30:57

171

Views

Limit of $\min \{a\in \mathbb{N} : \sum_{i=1}^{a}\frac1{i}\geq n\}$ equals $e$

Published on 25 Oct 2020 - 10:30

score 342 · Answer 5 · 2020-10-28 20:56:50

342

Views

Connection between exponential function as repeated multiplication and $\lim_{n \to \infty} (1 + \frac{1}{n})^n$ (also known as compund interest)

Published on 28 Oct 2020 - 20:56

score 134 · Answer 6 · 2020-10-29 04:08:04

134

Views

Use Euler's Formula to prove the following equation $ y = Ae^{\sqrt{\lambda}ix} + Be^{-\sqrt{\lambda}ix} $

Published on 29 Oct 2020 - 4:08

score 61 · Answer 7 · 2020-10-29 14:50:55

61

Views

Is there a closed form for $S=\sum_{n=1}^\infty\big(e-(1+1/n)^{n+1/2}\big)$?

Published on 29 Oct 2020 - 14:50

score 179 · Answer 8 · 2020-11-05 10:54:03

179

Views

Why is $e$ irrational?

Published on 05 Nov 2020 - 10:54

score 44 · Answer 9 · 2020-11-13 11:46:19

44

Views

Intuition for $e$ and natural logs

Published on 13 Nov 2020 - 11:46

score 157 · Answer 10 · 2020-11-22 16:37:36

157

Views

Three inequalities for number $e$: $\frac{e}{2n+2}<e-\left(1+\frac1n\right)^n<\frac{e}{2n+1}<\frac3{2n}$

Published on 22 Nov 2020 - 16:37

score 147 · Answer 11 · 2020-12-04 00:00:29

147

Views

How to show that $a_n=\left(1+\frac{1}{n}\right)^n$ monotonic growing

Published on 04 Dec 2020 - 0:00

score 39 · Answer 12 · 2020-12-04 18:25:11

39

Views

Fraction of even numbers in decimal expansion of $\pi$ and $e$.

Published on 04 Dec 2020 - 18:25

score 128 · Answer 13 · 2020-12-10 12:52:33

128

Views

Where does these nice patterns come from?

Published on 10 Dec 2020 - 12:52

score 898 · Answer 14 · 2020-12-17 14:33:48

898

Views

Imaginary interest rates

Published on 17 Dec 2020 - 14:33

score 57 · Answer 15 · 2020-12-20 17:47:41

57

Views

Why doesn't Euler's $e$ in the continuous interest formula show the exponent $n$?

Published on 20 Dec 2020 - 17:47

List Question

Why is $(e^{2πi})^i$ different from $(e^i)^{2πi}$

Strange similar approximations of pi and e

Using the number e to find the limit of a sequence

Limit of $\min \{a\in \mathbb{N} : \sum_{i=1}^{a}\frac1{i}\geq n\}$ equals $e$

Connection between exponential function as repeated multiplication and $\lim_{n \to \infty} (1 + \frac{1}{n})^n$ (also known as compund interest)

Use Euler's Formula to prove the following equation $ y = Ae^{\sqrt{\lambda}ix} + Be^{-\sqrt{\lambda}ix} $

Is there a closed form for $S=\sum_{n=1}^\infty\big(e-(1+1/n)^{n+1/2}\big)$?

Why is $e$ irrational?

Intuition for $e$ and natural logs

Three inequalities for number $e$: $\frac{e}{2n+2}<e-\left(1+\frac1n\right)^n<\frac{e}{2n+1}<\frac3{2n}$

How to show that $a_n=\left(1+\frac{1}{n}\right)^n$ monotonic growing

Fraction of even numbers in decimal expansion of $\pi$ and $e$.

Where does these nice patterns come from?

Imaginary interest rates

Why doesn't Euler's $e$ in the continuous interest formula show the exponent $n$?

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