What is the factorial of 0 added to infinity

What is the factorial of 0 added to infinity

It's infinite
(factorial) why = 1? Is there a factorial for 0.5
0! It's artificial
Because (n-1)! * n = n! When n = 1, 0! * 1 = 1! = 1, that is, 0! = 1,
This is for the sake of calculation
[for example: calculate combin (n, m) = n! / (n-m)!]. When n = m, combin (n, m) = n! / 0! Is n! In numerical value, so it is necessary to specify 0! As 1]
0.5 has no factorial. Only natural numbers and 0 have factorial. Other numbers have no factorial
It's a mistake.... 0.5 has a factorial, which is equal to the root sign (PI divided by 4)
Given the function f (x) = 2x + alnx-2. (1) if the tangent of curve y = f (x) at point P (1, f (1)) is perpendicular to the straight line y = 13X + 1, find the value of real number a; (2) under the condition of (1), find the monotone interval of function f (x)
(1) ∵ f (x) = 2x + alnx-2 has the definition domain of (0, + ∞), ∵ f '(x) = - 2x2 + ax; the tangent of the curve y = f (x) at point P (1, f (1)) is perpendicular to the straight line y = 13X + 1, ∵ f' (1) = - 212 + A1; ∵ a = - 1, that is, the value of a is - 1; (2) from (1), a = - 1, ∵ f (x) = 2x-lnx-2, the definition domain is (0, + ∞); ∵ f '(x) = - 2x2-lx = - x + 2x2; ∵ x ∈ (0, x);