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Relation between Coefficient and Indices of x and y

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Question

Find the greatest coefficient of the expansion of $(a + b)^{n}$ , if the sum of all the coefficients is equal to $4096$ .

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Solution

sum of the coefficients can be find by replacing a,b with $1$
$⟹ 2^{n} = 4096$
$⟹ n = 12$
$⟹$ greatest coefficient is $^{12} C_{6} = 3564$

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