№1982
\[\begin{array}{l}
N = \frac{{\sqrt 2 {\pi ^{\frac{3}{2}}}}}{{4\Gamma {{\left( {\frac{3}{4}} \right)}^2}}} = \frac{{\pi \cdot G}}{2} = \frac{1}{4}{\rm B}\left( {\frac{1}{4},\frac{1}{2}} \right). \hfill \\
\Gamma {\text{ - гамма - функция;}} \hfill \\
G{\text{ - постоянная Гаусса;}} \hfill \\
{\rm B}{\text{ - бета - функция}}{\text{.}} \hfill \\
{\text{Докажите}}{\text{, что }}1 + \frac{{1 + \frac{{1 + \frac{{1 + \frac{{1 + ...}}{{2 + 3/7}}}}{{2 + 3/5}}}}{{2 + 3/3}}}}{{2 + 3/1}} = N. \hfill \\
{a_k} = 2 + \frac{3}{{2k - 1}}. \hfill \\
\end{array}\]
Your solution
comments
Igore
847 days ago
Igore
815 days ago
\[{\text{Also }}N = {\left( {\int\limits_0^1 {\sqrt {\sin \pi x} dx} } \right)^{ - 1}}.\]