The coefficients of xp and xq (p and q are positive integers) in the expansion of (1+ x )p+q are

Question

The coefficients of xp and xq (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

Tardigrade Admin · Accepted Answer

We have tp + 1 = p + qCp xp and tq + 1 = p+qCq xq p + qCp = p + qCq. [ Remember nCr = nCn- r ]

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

equal

equal with opposite signs

reciprocals of each other

none of these

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 $^{n} C_{r} =^{n} C_{n - r}$ ]

Q. The coefficients of xp and xq (p and q are positive integers) in the expansion of (1+x)p+q are