The fourth term in the expansion of $(1 - 2x)^{3/2}$ is:

If $x > \sqrt{3}$ and $\frac{x^2+1}{(x^2+2)(x^2+3)}$ is expanded in terms of powers of $x^{-2}$,then the coefficient of $x^{-8}$ is

The sum of the series $\frac{3}{4 \cdot 8} - \frac{3 \cdot 5}{4 \cdot 8 \cdot 12} + \frac{3 \cdot 5 \cdot 7}{4 \cdot 8 \cdot 12 \cdot 16} - \dots$ is:

If $x = \frac{2 \cdot 5}{(2!) 3} + \frac{2 \cdot 5 \cdot 7}{(3!) 3^2} + \frac{2 \cdot 5 \cdot 7 \cdot 9}{(4!) 3^3} + \dots$,then $x^2 + 8x + 8 = $

If $|x| < \frac{1}{2}$,then the coefficient of $x^r$ in the expansion of $\frac{1+2x}{(1-2x)^2}$ is

If $5|b| < 2|a|$,then the $4^{th}$ term in the expansion of $(2a + 5b)^{-4}$ is