Given $f\left(x\right)=x^3 \sin\left(x^2\right)$, find the value of $f^{\left(25\right)}\left(0\right)$, the $25^{th}$ derivative of $f$ at $x=0$.
*Give your answer using “$!$” (factorial)

Find the exact value of the sum of following infinite series:
$$\frac{\pi}{3!}-\frac{\pi^3}{5!}+\frac{\pi^5}{7!}-\frac{\pi^7}{9!}+\cdots$$

Find the exact value of the sum of following infinite series:
$$\frac{1}{1\left(2\right)}+\frac{1}{3\left(4\right)}+\frac{1}{5\left(6\right)}+\frac{1}{7\left(8\right)}\cdots$$