The total number of terms in the expansion of

In $(1+x)^{2 n}-(1-x)^{2 n}$

Since

$(1+x)^{2 n}={ }^{2 n} C_{0}+{ }^{2 n} C_{1} x+\ldots \ldots+{ }^{2 n} C_{2 n} x^{2 n}$

$(1-x)^{2 n}={ }^{2 n} C_{0}-{ }^{2 n} C_{1} x+\ldots \ldots+{ }^{2 n} C_{2 n} x^{2 n}$

Subtracting above two,

i. e. $(1+x)^{2 n}-(1-x)^{2 n}=2\left[{ }^{2 n} C_{1} x+{ }^{2 n} C_{3} x^{3}+\ldots{ }^{2 n} C_{2 n-1} x^{2 n-1}\right]$

i. e. number of terms here $=2 \times \frac{n}{2}($ odd from $2 n$ is $n)$

$=n$