Question

若abc三个正整数成等差数列,公差d不等于0自然数n大于等于2求证a^n+c^n>2b^n

Answer 1

不妨设a＞b＞c

当n=2时明显成立.

假设当n=k(k>=2),有(a'k+c'k)/2>=[(a+c)/2]'k

当n=k+1时,[(a+c)/2]'(k+1)=[(a+c)/2]'k*[(a+c)/2]