If the sum of the coefficients in the expansion of (x + y)n is 4096, then the greatest coefficient in the expansion is _____________.
Answer (integer)
924
Solution
(x + y)<sup>n</sup> $\Rightarrow$ 2<sup>n</sup> = 4096<br><br>2<sup>10</sup> = 1024 $\times$ 2<br><br>$\Rightarrow$ 2<sup>n</sup> = 2<sup>12</sup><br><br>2<sup>11</sup> = 2048<br><br>n = 12<br><br>2<sup>12</sup> = 4096<br><br>$${}^{12}{C_6}={{12 \times 11 \times 10 \times 9 \times 8 \times 7} \over {6 \times 5 \times 4 \times 3 \times 2 \times 1}}$$<br><br>$= 11 \times 3 \times 4 \times 7$<br><br>$= 924$
About this question
Subject: Mathematics · Chapter: Binomial Theorem · Topic: Binomial Expansion
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