Question

If the sum of the coeficients in the expansion of $(a+b{)}^n$ is 4096, then the greatest coefficient in the

expansion is.

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Answer 1

Sum of the coefficients in the expansion of $(a+b{)}^n$ = $2^n$ = 4096 = $2^{12}$

⇒ n = 12

Since n is even, there will be only one middle term, which $t_7$.

⇒ The greatest coefficient = ${}^{12}{C}_6$

= $\frac{12!}{6!\times 6!}$

= 924