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Binomial Coefficients

In the expans...

Question

In the expansion of ${(1 + a)}^{m + n}$ , prove that coefficients of $a^{m}$ and $a^{n}$ are equal.

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Solution

$(1 + a)^{m + n}$
Coefficient of $a^{m} =^{m + n} C_{m}$
$= m + n$
Coefficient of $a^{n} =^{m + n} C_{n}$
$^{n} C_{x} =^{n} C_{(n - x)}$ Property
Both are equal.
Hence proved

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