First slide

Binomial theorem for positive integral Index

Question

Suppose $p \in R .$ If the fourth term in the expansion of ${(p x + \frac{1}{x})}^{n}$ is $\frac{5}{2}$ then $(n, p)$ is equal to:

Moderate

A

(5, 1/2)
B

(6, 1/2)
C

(8, 1/2)
D

(10, 1/2)

Solution

$\begin{array}{l} T_{4} =^{n} C_{3} (p x)^{n - 3} {(\frac{1}{x})}^{3} =^{n} C_{3} p^{n - 3} x^{n - 6} = \frac{5}{2} \\ \Leftrightarrow n - 6 = 0 {and}^{6} C_{3} p^{3} = \frac{5}{2} \Leftrightarrow n = 6, p = 1 / 2 \end{array}$

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