Question

If $f( x )= x +\frac{ x ^2}{1 !}+\frac{ x ^3}{2 !}+\ldots \ldots \frac{ x ^{ n }}{( n -1) !}$, then $f(0)+f^{\prime}(0)+f^{\prime \prime}(0)+\ldots \ldots . .+f^{\prime \prime \prime \prime \ldots . . . n \text { ntimes }}(0)$ is equal to -

• A. $\frac{ n ( n +1)}{2}$
• B. $\frac{\left( n ^2+1\right)}{2}$
• C. $\left(\frac{ n ( n +1)}{2}\right)^2$
• D. $\frac{n(n+1)(2 n+1)}{6}$

Answer 1

Answer: (A)

Correct answer is (a) $\frac{ n ( n +1)}{2}$