Дано
$$frac{left(2 nright)! left(left(2 nright)!right)!}{2^{2 n} n!^{2} left(left(2 n + 1right)!right)!}$$
Подстановка условия
$$frac{left(2 nright)! left(left(2 nright)!right)!}{2^{2 n} n!^{2} left(left(2 n + 1right)!right)!}$$
(factorial(2*(-3/2))*factorial(factorial(2*(-3/2))))/((factorial(factorial(2*(-3/2) + 1))*factorial((-3/2))^2)*2^(2*(-3/2)))
$$frac{left(2 (-3/2)right)! left(left(2 (-3/2)right)!right)!}{2^{2 (-3/2)} (-3/2)!^{2} left(left(2 (-3/2) + 1right)!right)!}$$
(factorial(2*(-3)/2)*factorial(factorial(2*(-3)/2)))/((factorial(factorial(2*(-3)/2 + 1))*factorial(-3/2)^2)*2^(2*(-3)/2))
$$frac{left(frac{-6}{2}right)! left(left(frac{-6}{2}right)!right)!}{2^{frac{-6}{2}} left(- frac{3}{2}right)!^{2} left(left(frac{-6}{2} + 1right)!right)!}$$
$$tilde{infty}$$
Степени
$$frac{2^{- 2 n} left(2 nright)! left(left(2 nright)!right)!}{n!^{2} left(left(2 n + 1right)!right)!}$$
-n
4 *(2*n)!*((2*n)!)!
——————–
2
n! *((1 + 2*n)!)!
$$frac{4^{- n} left(2 nright)! left(left(2 nright)!right)!}{n!^{2} left(left(2 n + 1right)!right)!}$$
Численный ответ
2.0^(-2.0*n)*factorial(2*n)*factorial(factorial(2*n))/(factorial(n)^2*factorial(factorial(2*n + 1)))
Рациональный знаменатель
$$frac{2^{- 2 n} left(2 nright)! left(left(2 nright)!right)!}{n!^{2} left(left(2 n + 1right)!right)!}$$
Объединение рациональных выражений
$$frac{2^{- 2 n} left(2 nright)! left(left(2 nright)!right)!}{n!^{2} left(left(2 n + 1right)!right)!}$$
Общее упрощение
(-1/2 + n)!*((2*n)!)!
—————————–
____
/ pi *n!*((1 + 2*n)*(2*n)!)!
$$frac{left(n – frac{1}{2}right)! left(left(2 nright)!right)!}{sqrt{pi} n! left(left(2 n + 1right) left(2 nright)!right)!}$$
Соберем выражение
$$frac{2^{- 2 n} left(2 nright)! left(left(2 nright)!right)!}{n!^{2} left(left(2 n + 1right)!right)!}$$
Комбинаторика
-2*n 1 + 2*n
2 *2 *(-1/2 + n)!*((2*n)!)!
————————————
____
2*/ pi *n!*(2*n*(2*n)! + (2*n)!)!
$$frac{2^{- 2 n} 2^{2 n + 1} left(n – frac{1}{2}right)! left(left(2 nright)!right)!}{2 sqrt{pi} n! left(2 n left(2 nright)! + left(2 nright)!right)!}$$
Общий знаменатель
-2*n
2 *(2*n)!*((2*n)!)!
———————-
2
n! *((1 + 2*n)!)!
$$frac{2^{- 2 n} left(2 nright)! left(left(2 nright)!right)!}{n!^{2} left(left(2 n + 1right)!right)!}$$
Раскрыть выражение
-2*n
2 *(2*n)!*((2*n)!)!
———————-
2
n! *((2*n + 1)!)!
$$frac{2^{- 2 n} left(2 nright)! left(left(2 nright)!right)!}{n!^{2} left(left(2 n + 1right)!right)!}$$
