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Perpendicular Bisector

In the expans...

Question

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

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Solution

coeff of $A^{m} =^{m + m} C_{m} = \frac{∠ m + n}{∠ m ∠ m} . . . (1)$
coeff of $a^{n} =^{m + n} C_{n} = \frac{∠ m + n}{∠ n ∠ m} . . . (2)$
$∴$ coeff of $a^{m} =$ coeff of $a^{n}$

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