Question

The coefficients of $x^p$ and $x^q$ (p and q are positive integers) in the expansion of $(1+ x )^{p+q}$ are

• A. equal
• B. equal with opposite signs
• C. reciprocals of each other
• D. none of these

Answer 1

Answer: (A)

equal

Answer 2

We have $t_{p + 1} = {^{p + q}C_p}\, x^p$ and $t_{q + 1} = {^{p+q}C_q} \, x^q \, {^{p + q}C_p }= {^{p + q}C_q}$. [ Remember $^nC_r = {^nC_{n- r}}$ ]