Which of following is/are true? In expansion $(x^2+1+\frac{1}{x^2})^n$ , n $\in \mathbb{N}$ 
1.number of terms is $2n+1$
2.coefficient of constant term is $2^{n-1}$
3.coefficient of $x^{2n-2}$ is $n$
4.coefficient of $x^2$ is $n$
I tried by taking lcm and writing as $\frac{(1+x^2+x^4)^n}{x^{2n}}$. How do i proceed? thanks

Usign the Newton formula we have:
$\left(x^2+1+\frac{1}{x^2}\right)^n=(x^2+1)^n+n(x^2+1)^{n-1}\cdot\frac{1}{x^2}\cdots\left(\frac{1}{x^2}\right)^n$
$=x^{2n}+n(x^2)^{n-1}\cdot 1\cdots 1+n+n(x^2+1)^{n-1}\cdot\frac{1}{x^2}\cdots\left(\frac{1}{x^2}\right)^n$
$=x^{2n}+n(x)^{2n-2}\cdot 1\cdots 1+n+n(x^2+1)^{n-1}\cdot\frac{1}{x^2}\cdots\left(\frac{1}{x^2}\right)^n$
i.e., concule that 3. is correct.
