If `f(x)=x^(n),"n" epsilon N`, then the value of `f(1)-(f^(')(1))/(1!)+(f^(")(1))/(2!)-(f^''')(1)/(3!)+…+(-1)^(n)(f^(n)(1))/(n!)` is

Options

A. `1`
B. `2^(n)`
C. `2^(n-1)`
D. `0`

Answer

D

Explanation

`f(x)=x^(n)`
`:.f(1)-(f^(')(1))/(1!)+(f^(")(1))/(2!)+…+((-1)^(n)f^(n)(1))/(n!)`
`=1-n/(1!)+(n(n-1))/(2!)-………+(-1)^(n)(n!)/(n!)`
`=^(n)C_(0)-^(n)C_(1)+^(n)C_(2)-……..+(-1)^(n) .^(n)C_(n)=0`