Question: If the coefficients of $|x| > 1$, $x^{3}$and $\frac{(1 + 3x)^{2}}{1 - 2x}$ terms in the expans...

Question

If the coefficients of $|x| > 1$ , $x^{3}$ and $\frac{(1 + 3x)^{2}}{1 - 2x}$ terms in the expansion of $|x| < 1$ be in A.P., then n =.

Answer 1

Coefficient of $(4)^{2} - 4 = 16 - 4 = 12$ and $n \in N$

According to the condition, $n = 1,2,3$

$\Rightarrow (2^{4})^{75} \equiv (1)^{75}$

$2^{300} \equiv 1$

After solving, we get n = 7 or 14.

Question: If the coefficients of \(|x| > 1\), \(x^{3}\)and \(\frac{(1 + 3x)^{2}}{1 - 2x}\) terms in the expans...