f-x-x-n-find-A-f-1-f-1-1-f-1-2-f-1-3-f-n-1-n-

Question Number 191582 by Matica last updated on 26/Apr/23

f (x) = x^{n} . f i n d

A = f (1) + \frac{f^{^{'}} (1)}{1} + \frac{f^{^{″}} (1)}{2} + \frac{f^{^{‴}} (1)}{3} + \dots + \frac{f^{(n)} (1)}{n}

Answered by aleks041103 last updated on 27/Apr/23

f^{(k)} (x) = {(x^{n})}^{(k)} = {\begin{cases} \frac{n!}{(n - k)!} x^{n - k}, k = 0, 1, \dots, n \\ 0, k > n \end{cases}

\Rightarrow A = 1 + \underset{k = 1}{\sum^{n}} \frac{n!}{k (n - k)!}