Question

If f(x) = $1-x+x^2-x^3+.......+x^{16}-x^{17},$ then the coefficient of $x^2$ in f(x - 1) is

• A. 816
• B. - 816
• C. 618
• D. - 618

Answer 1

The correct option is A 816

$f\left(x\right)=\frac{1-x^{18}}{1+x}\Rightarrow f(x-1)=\frac{1-(x-1{)}^{18}}{x}$
Coeff. Of $x^2$ in f(x-1) = coeff. of $x^3$ in NR = ${}^{18}{C}_3=816$