Question

If f(x) = xⁿ , then the value of

f(1) - f '(1)/1! + f "(1)/2! - f '''(1)/3! + ...... + ((- 1)ⁿfⁿ(1))/n! is

(a) 2^{n – 1} 

(b) 0 

(c) 1 

(d) 2ⁿ.

Answer 1

Putting x = –1 in both side of * we get
0 = C₀ – C₁ + C₂ – C₃ + ...