What will be the $n^{th}$ term of this given series? Given series is:
$$1+\frac{1\times x^2}{2\times 4}+\frac{1\times 3\times 5\times x^4}{2\times 4\times 6\times 8}+\frac{1\times 3\times 5\times 7\times 9\times x^6}{2\times 4\times 6\times 8\times 10\times 12}+.....\infty$$
I need to find it's $n^{th}$ term but am having trouble in dealing with increasing number of multiples in each step. Kindly Guide in How to proceed

Hint: Your $n$th term (counting the first non-$1$ term as the first term and excepting the $0$th term) looks to be
$$x^{2n}\frac{1\times 3 \times \cdots \times  (4n-3)}{2\times 4\times \cdots \times (4n)}.$$
This equals
$$x^{2n}\frac{1\times 2 \times \cdots \times  (4n-2)}{\left(2\times 4\times \cdots \times (4n-2)\right)\left(2\times 4\times \cdots \times (4n)\right)}.$$
How can we represent this in terms of factorials?
