用二项式定理证明2∧n>n^2

Question

用二项式定理证明2∧n>n^2

Answer 1

n .1...2...3...4...52^n...2...4...8...16..32n^2...1...4...9...16..25,下面用二项式定理证明n>=5时2^n>n^2,事实上,2^n=(1+1)^n=C(n,0)+C(n,1)+C(n,2)+C(n,3)+C(n,4)+C(n,5)+……>=1+n+n(n-1)/2+n(n-1)(n-2)/6+n(n...