Suppose p ∈ R. If the fourth term in the expansion of px+1xn is 52 then (n, p) is equal to:

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:

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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