In the expansion of (1+ a)m+n , prove that coefficients of am and an – InterviewSolution

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1.

In the expansion of (1+ a)m+n , prove that coefficients of am and an are equal.

Answer»

We have T_{r + 1} = ^{m + n}C_r a^r

⇒ Coefficient of a^r = ^{m + n}C_r

∴ Coefficient of a^m = ^{m + n}C_m

Similarly, coefficient of aⁿ = ^{m + n}C_n

= ^{m + n}C_{(m + n) - n}

= ^{m + n}C_m

∴ Coefficient of a^m= coefficient of aⁿ

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