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MathFail
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26
A Tough Series: $\sum_{n=0}^\infty2^na_{n+1}\sqrt{a_n}=\frac{\Gamma^2(\frac14)-4\cdot\Gamma^2(\frac34)}{8\sqrt{2\pi}}$
Jun 19, 2023
20
Integral of $\displaystyle \int\sqrt{x\sqrt{x\sqrt{x...\sqrt{x}}}}\,dx$ where $x$ is repeated $n$ times
Aug 29, 2022
19
How to prove $\frac{\sqrt{5}+1}{2}>\log_23$?
Jun 7, 2023
16
Sophomore's Eternal Dream $\int_0^1\cdots\int_0^1 (t_1t_2\cdots t_n)^{t_1t_2\cdots t_n} dt_1 dt_2\cdots dt_n$
Jul 2, 2022
14
Why does limit: $\lim_{x\to\infty}\prod\limits^{\lfloor x\rfloor}_{n=1}\frac{\lceil x\rceil}{\lfloor x\rfloor}=e$?
Jun 9, 2023
13
How to compute: $\dfrac{2\cos 80^\circ-\sin 70^\circ}{\cos 70^\circ}$
Jun 10, 2023
13
Show that $\int_0^\pi \frac{x\cos x \sinh x}{\sin^2x+\sinh^2x}dx=\frac{\pi}{2}\ln\left(\frac{e^\pi+1}{e^\pi-1}\right)$
Jun 19, 2023
12
Tough integral: $\int_0^1 \frac{\arctan(x^{3+\sqrt{8}})}{1+x^2}dx$
Jul 26, 2022
11
Proof check: If $G$ is an infinite group, then it has infinite number of subgroups. [duplicate]
Feb 28, 2023
10
Use Abel-Plana formula to compute $\int_0^\infty \frac{\arctan(t)}{e^{2\pi t}-1} dt $
Jul 13, 2022
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6
Weird output when plot piecewise continuous and periodic functions