1/a+1/b=1
ab = a+b ≥2√ab
√ab ≥2
ab-a-b = 0
ab-a-b+1 = (a-1)(b-1) = 1
(a+b)^n-a^n-b^n +1
=(a^n-1)(b^n-1)
= (a-1)(b-1) (a^(n-1)+a^(n-2)+...+a+1)(b^(n-1)+b^(n-2)+...+b+1)
= (a^(n-1)+a^(n-2)+...+a+1)(b^(n-1)+b^(n-2)+...+b+1)
≥ [(ab)^(n-1)/2 + (ab)^(n-2)/2+...+ab^(1/2)+1]^2
≥[2^(n-1)+2^(n-2)+...+2+1]^2
= (2^n-1)^2
= 2^(2n)-2^(n+1) +1
(a+b)^n-a^n-b^n ≥ 2^(2n)-2^(n+1)