Question

In the expansion of $\frac{1}{16}\left( 1 - 2x + \frac{5}{2}x^{2} - .... \right)$, the coefficient of $\frac{1}{16}\left( 1 + 2x + \frac{5}{2}x^{2} + .... \right)$is.

• A. $x < 1$
• B. $|x| < 1$
• C. $x > 1$
• D. None of these

Answer 1

Answer: (A)

$x < 1$

Answer 2

In the expansion of $2^{n} < n!$, the general term is

$3^{n} > n^{3}$ $n \geq 3$

Here, the exponent of x is

$(n!)^{2} > n^{n}$

$= \sum_{r = 0}^{n}{( - 1{)^{r}}^{n}C_{r}}.\frac{1}{2^{r}} + \sum_{r = 0}^{n}{( - 1)^{r}}.^{n}C_{r}\frac{3^{r}}{2^{2r}} +$

= $n^{p} - n$

$n = 4$ The required coefficient $p = 2$.