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Finding Remainder of Numbers of the Form a^b

If the sum of...

Question

If the sum of the coefficients of first half terms in the expansion of $(x + y)^{n}$ is $256$ , where $n$ is odd positive integer, then the greatest coefficient in the expansion is

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Solution

The sum of the coefficients of first half of the terms
$2^{n - 1} = 256 \Rightarrow n = 9$
So, the greatest coefficient
$^{9} C_{5} =^{9} C_{4} = \frac{9 \times 8 \times 7 \times 6}{4!} = 126$

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Finding Remainder of Numbers of the Form a^b

Standard XII Mathematics

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