Question

Q. If f(x)= ∑_(n=0)^∞▒n^(n⁄2)/n! x^(n ), then f^6(0)=?

Answer 1

$$u_n = \frac{f^{(n)}(0)}{n!}x^n=\frac{n^{\frac{n}{2}}}{n!}x^n$$

$$for \space \space n=6$$

$$u_6 = \frac{f^{(6)}(0)}{6!}x^6=\frac{6^{\frac{6}{2}}}{6!}x^6$$ $$f^{(6)}(0)=6^{\frac{6}{2}}=6^3=216$$