Question

高数不等式证明题证当a＞1时,a^(n+1)+1/a^(n+1)＞a^n+1/a^n(a的n+1次方加上它的倒数大于a的

Answer 1

a^(n+1)+1/a^(n+1)-a^n-1/a^n

=a^n（a-1）-1/a^(n+1)*(a-1)

=(a-1)(a^n-1/a^(n+1))

很明显a^n-1/a^(n+1)＞0

∴不等式成立