Find the closed form of $$x+ \frac {2}{1\cdot 3} x^3 + \frac {2\cdot 4}{1\cdot 3\cdot 5} x^5 + \dots \quad \forall x \in (0, 1)$$
My approach:
Clearly we can see the formation of factorial in the denominator. so the series becomes-
$$x+ \frac {2^2}{3!} x^3 + \frac {2^2\cdot 4^2}{5!} x^5 + \dots $$
I cannot remember a series like that. then the other approach left is integration. now what to integrate, I am confused about that. I am just a beginner in this.