We know, (a+b)n=‌nC0⋅an+‌nC1⋅an−1⋅b+...+‌nCn⋅bn Remember to find sum of coefficient of binomial expansion we ave to put 1 in place of all the variable. So put a=b=1 ∴2n=‌nC0+‌nC1+‌nC2...+‌nCn According to question, 2n=4096=212 ⇒n=12 So (a+b)n=(a+b)12 Here n=12 is even so formula for greatest term is T‌
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For n=12, greatest term T6+1=‌12C6⋅a6⋅b6 ∴ Coefficient of the greatest term =‌12C6=‌