Question

If

f (n)(0) = (n + 1)!
for
n = 0, 1, 2, ,
find the Maclaurin series for f.

Answer 1

The Maclaurin series for f(n) is 1.

Step-by-step explanation:

The Maclaurin series for a function can be found using the formula: f(x) = f(0) + f'(0)x + f''(0)x^2/2! + f'''(0)x^3/3! + ...

In this case, f(0) = (0+1)! = 1, f'(0) = d/dx((0+1)!) = d/dx(1) = 0, f''(0) = d^2/dx^2((0+1)!) = d^2/dx^2(1) = 0, and so on.

Using these values, the Maclaurin series for f(n) is: f(n)(x) = 1 + 0x + 0x^2/2! + 0x^3/3! + ... = 1.

Answer 2

f (n)=(n+1)!
use that in the sum S where f^n represents nah derivative but u have that already so choose follow formula