If the third term in the binomial expansion of $(1 + x)^m$ is $-\frac{1}{8}x^2$,then the rational value of $m$ is

The first four terms in the expansion of $(1 - x)^{3/2}$ are

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

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

If $\alpha = \frac{5}{2! \times 3} + \frac{5 \times 7}{3! \times 3^2} + \frac{5 \times 7 \times 9}{4! \times 3^3} + \ldots$,then $\alpha^2 + 4\alpha =$

If $x = \frac{3}{4 \cdot 8} + \frac{3 \cdot 5}{4 \cdot 8 \cdot 12} + \frac{3 \cdot 5 \cdot 7}{4 \cdot 8 \cdot 12 \cdot 16} + \ldots$,then $2x^2 + 5x =$