Question

The coefficient of x^p and x^q (p and q are positive integers) in the expansion of (1 + x)^{p + q} are ______.

Options

• Equal

• Equal with opposite signs

• Reciprocal of each other

• None of these

Answer 1

The coefficient of x^p and x^q (p and q are positive integers) in the expansion of (1 + x)^{p + q} are equal.

Explanation:

Coefficient of x p and x q in the expansion of (1 + x)^{p + q} are ^{p + q}C_p and ^{p + q}C_q 

And ^{p + q}C_p and ^{p + q}C_q  = `("p" + "q")/(("p")("q"))`