Question

Show $(-1)^{n}\ln\left[ \frac{n(n+2)}{n^2-n+1} \right]=3\frac{(-1)^{n}}{n}+\mathcal{O}\left( \frac{1}{n^2}\right) $

score 21 · Answer 1 · 2016-07-23 09:01:10

21

Views

Show $(-1)^{n}\ln\left[ \frac{n(n+2)}{n^2-n+1} \right]=3\frac{(-1)^{n}}{n}+\mathcal{O}\left( \frac{1}{n^2}\right) $

Published on 23 Jul 2016 - 9:01

score 80 · Answer 2 · 2026-03-25 23:37:32

80

Views

What is the proof that $\int e^{-x^2} \cdot dx$ is not elementary.

Published on 25 Mar 2026 - 23:37

score 44 · Answer 3 · 2016-07-23 10:20:34

44

Views

Show $ \frac{(-1)^{n}}{n-\ln(n)}=\frac{(-1)^{n}}{n}+\mathcal{O}\left(\frac{\ln(n)}{n^{2}} \right) $

Published on 23 Jul 2016 - 10:20

score 35 · Answer 4 · 2016-07-23 12:56:42

Show that $\frac{(-1)^{n}}{\left(\ln(n)+(-1)^{n}\right)^{2}}=\frac{(-1)^{n}}{\ln^{2}(n)}+v_n\quad \left( v_n\sim -\frac{2}{\ln^{3}(n)} \right) $

score 1.2k · Answer 5 · 2016-07-24 03:35:17

1.2k

Views

Taylor series of a square matrix

Published on 24 Jul 2016 - 3:35

score 92 · Answer 6 · 2016-07-24 06:17:27

92

Views

Taylor expansion with several variables

Published on 24 Jul 2016 - 6:17

score 42 · Answer 7 · 2016-07-24 11:38:53

42

Views

Show that $(-1)^{n}\left( (n+1)^{\frac{1}{n+1}}-n^{\frac{1}{n}}\right)=\mathcal{O}\left(\frac{\ln(n)}{n} \right) $

Published on 24 Jul 2016 - 11:38

score 51 · Answer 8 · 2016-07-24 13:11:07

Show $\cos\left( \pi n^{2}\ln\left(\frac{n}{n-1} \right) \right)=(-1)^{n+1}\frac{\pi}{3n}+\mathcal{O}\left( \frac{1}{n^2}\right) $

score 31 · Answer 9 · 2016-07-24 16:18:23

31

Views

Show $\sin\left(2\pi\sqrt{n^2+(-1)^{n}} \right)=\frac{(-1)^{n}\pi}{n}+\mathcal{O}\left( \frac{1}{n^2}\right) $

Published on 24 Jul 2016 - 16:18

score 75 · Answer 10 · 2016-07-24 20:34:32

75

Views

Show $\ln\left(\frac{n+(-1)^{n}\sqrt{n}+a}{n+(-1)^{n}\sqrt{n}+b} \right)=\frac{a-b}{n}+\mathcal{O}\left(\frac{1}{n^2} \right) $

Published on 24 Jul 2016 - 20:34

score 91 · Answer 11 · 2016-07-25 00:49:34

91

Views

Taylor expansion of $\left(\int_{t}^{t+\Delta t}a(t')dt'\right)$

Published on 25 Jul 2016 - 0:49

score 63 · Answer 12 · 2016-07-25 10:56:14

63

Views

nature of series $\sum_{n\geq 0}(-1)^{n}u_n $

Published on 25 Jul 2016 - 10:56

score 4k · Answer 13 · 2016-07-25 11:11:43

4k

Views

Taylor-polynomial of $f(x)=\log(\cos(x))$

Published on 25 Jul 2016 - 11:11

score 39 · Answer 14 · 2016-07-25 13:15:25

39

Views

Is $\frac{1}{3!}\frac{d^2a}{dt^2}(t) \Delta t^3 < \frac{1}{2}\frac{da}{dt}(t) \Delta t^2$ always true for $\Delta t$ small than one?

Published on 25 Jul 2016 - 13:15

score 2.8k · Answer 15 · 2016-07-25 19:17:47

2.8k

Views

Taylor-polynomial of function $f(x) = e^{x}*\sin(2x)$

Published on 25 Jul 2016 - 19:17

List Question

Show $(-1)^{n}\ln\left[ \frac{n(n+2)}{n^2-n+1} \right]=3\frac{(-1)^{n}}{n}+\mathcal{O}\left( \frac{1}{n^2}\right) $

What is the proof that $\int e^{-x^2} \cdot dx$ is not elementary.

Show $ \frac{(-1)^{n}}{n-\ln(n)}=\frac{(-1)^{n}}{n}+\mathcal{O}\left(\frac{\ln(n)}{n^{2}} \right) $

Show that $\frac{(-1)^{n}}{\left(\ln(n)+(-1)^{n}\right)^{2}}=\frac{(-1)^{n}}{\ln^{2}(n)}+v_n\quad \left( v_n\sim -\frac{2}{\ln^{3}(n)} \right) $

Taylor series of a square matrix

Taylor expansion with several variables

Show that $(-1)^{n}\left( (n+1)^{\frac{1}{n+1}}-n^{\frac{1}{n}}\right)=\mathcal{O}\left(\frac{\ln(n)}{n} \right) $

Show $\cos\left( \pi n^{2}\ln\left(\frac{n}{n-1} \right) \right)=(-1)^{n+1}\frac{\pi}{3n}+\mathcal{O}\left( \frac{1}{n^2}\right) $

Show $\sin\left(2\pi\sqrt{n^2+(-1)^{n}} \right)=\frac{(-1)^{n}\pi}{n}+\mathcal{O}\left( \frac{1}{n^2}\right) $

Show $\ln\left(\frac{n+(-1)^{n}\sqrt{n}+a}{n+(-1)^{n}\sqrt{n}+b} \right)=\frac{a-b}{n}+\mathcal{O}\left(\frac{1}{n^2} \right) $

Taylor expansion of $\left(\int_{t}^{t+\Delta t}a(t')dt'\right)$

nature of series $\sum_{n\geq 0}(-1)^{n}u_n $

Taylor-polynomial of $f(x)=\log(\cos(x))$

Is $\frac{1}{3!}\frac{d^2a}{dt^2}(t) \Delta t^3 < \frac{1}{2}\frac{da}{dt}(t) \Delta t^2$ always true for $\Delta t$ small than one?

Taylor-polynomial of function $f(x) = e^{x}*\sin(2x)$

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