Hi , sorry this may seem so easy but i'm just starting sage !
I want this code to show the answer, how can i do that ? how can i change the code ?
n=var('n)
f=factorial(2*n + 3)/factorial(n + 1)
f.simplify_factorial()
output is :
factorial(2*n + 3)/factorial(n + 1)
Sage offers various ways to express the desired product, using
Only the last one seems to keep the desired product expressed as a product of n + 2 terms.
sage: k, n = SR.var('k, n')
sage: factorial(2*n + 3)/factorial(n + 1)
factorial(2*n + 3)/factorial(n + 1)
sage: gamma(2*n + 4)/gamma(n + 2)
gamma(2*n + 4)/gamma(n + 2)
sage: falling_factorial(2*n + 3, n + 2)
gamma(2*n + 4)/gamma(n + 2)
sage: rising_factorial(n + 2, n + 2)
gamma(2*n + 4)/gamma(n + 2)
sage: product(k, k, n + 2, 2*n + 3)
factorial(2*n + 3)/factorial(n + 1)
sage: product(k, k, n + 2, 2*n + 3, hold=True)
product(k, k, n + 2, 2*n + 3)
Asked: 2021-04-10 17:38:56 +0200
Seen: 317 times
Last updated: Apr 11 '21
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Could you develop on what you mean by "the answer"?
The answer would look like this: $$(2n+3)(2n+2)(2n+1)(2n)(2n-1) \cdots (2n-n+2)$$ It would have $n+2$ factors. Not very useful, and I am not sure why it's needed.