If , then is equal…

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

If f(x)=x+x21!+x32!+⋯+xn(n−1)!f(x)=x+\frac{x^2}{1!}+\frac{x^3}{2!}+\cdots+\frac{x^n}{(n-1)!}, then f(0)+f′(0)+f′′(0)+⋯+f(n)(0)f(0)+f'(0)+f''(0)+\cdots+f^{(n)}(0) is equal to (1) n(n+1)2\frac{n(n+1)}{2} (2) n2+12\frac{n^2+1}{2} (3) (n(n+1)2)2\left(\frac{n(n+1)}{2}\right)^2 (4) n(n+1)(2n+1)6\frac{n(n+1)(2n+1)}{6}

Related theory

Browse the problem library