Did Euler guess the Basel problem’s solution to be $\\frac{\\pi^2}{6}$?
Mar 2, 2025 · I've been interested in the Basel problem and its famous solution $$ \\sum_{n=1}^{\\infty}{\\frac{1}{n^2}} = \\frac{\\pi^2}{6}. $$ Recently I saw this video along with a …
Prove that $\ln\bigl (\frac {2} {\sqrt {3}}+1\bigr) < (\frac {4} {3 ...
Feb 3, 2025 · Prove that $\ln\Bigl (\frac {2} {\sqrt {3}}+1\Bigr) < \frac {4} {3} - \frac {\pi} {6}$. I found out that this can be solved by using the function $\ln (1 + \sec x) - \sec^2 x + x$.
Why is $\sin (\pi/6) = 0.5$? - Mathematics Stack Exchange
Jun 9, 2014 · Why is $\\sin(30^\\circ)$ exactly $0.5,$ when it could be 0.49999 or something else? There must be an easy geometric explanation?
Proof of Sum of inverse squares Equaling $\pi^2/6$
Apr 16, 2021 · I will outline Euler's second proof of the Basel problem. If we start with the identity: $$ \frac {\sin (\pi x)} {\pi x}=\prod_ {n\geq 1}\left (1-\frac {x^2} { n^2 ...
How to refactor $\pi / 12$ into $\pi /4 - \pi /3$?
Aug 24, 2019 · 5 I'm assuming you are able to go from $\pi/4-\pi/6$ to $\pi/12$, but are asking about how to go the other way.
trigonometry - How to memorize the families that are $\sin$, $\cos ...
0 (1) Visualize it so you understand it (and don't have to memorize it): google image search for pi/6 But it's also good to develop " (2) skill of understanding" by being able to quickly come up with the …
Find the first four nonzero terms of the Taylor series for $\sin x ...
Jul 20, 2016 · What if it was a maclaurin series? My a would be 0, how would the rest of the problem change? I would do f (0) instead of f (pi/6), would I have just x, x^2, x^3 instead of x - pi/6, x - pi/6 …
how ** (1)** $ (2n-1)\pi/2 + (-1)^n\pi/3$ and ** (2)** $2n\pi±\pi/6 ...
Feb 4, 2016 · I have a question in my book which I don't understand how to proof. The question is Show that the two angles are indicated by the two following formulae - (1) $ (2n-1)\pi/2 + (-1)^n\pi/3$ and …
Converting $9e^ { (3+i\pi/6)}$ into cartesian form
Mar 23, 2021 · Converting $9e^ { (3+i\pi/6)}$ into cartesian form Ask Question Asked 4 years, 9 months ago Modified 4 years, 9 months ago
Is it possible to express $\sin \frac {\pi} {9}$ in terms of radicals?
I'm not sure what your question is. $\pi/9$ is an exact value. It is $\pi$ times $1/9$. Like $\pi$, $\pi/9$ is a transcendental number : I suggest Googling "transcendental number" or finding a good book …