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

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

AIEEEAIEEE 2002Binomial Theorem

Solution:

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 $^nC_r = {^nC_{n- r}}$ ]