Question

1.已知A,B,C为正数,N是正整数,且f(n)=lg[(An+Bn+Cn)/3],求证：2f(n)

Answer 1

1.2f(n)=lg[(A^n+B^n+C^n)^2/9] f(2n)=lg[(A^2n+B^2n+C^2n)/3] 只要使中括号里面的相减即可,即[(A^2n+B^2n+C^2n+2A^nB^n+2B^nC^n+2A^nC^n)-(3A^2n+3B^2n+3C^2n)]/9整理得-（2A^2n+2B^2n+2C^2n-2A^nB^n-2B^nC^n-2A^nC^n）/9即-[(A^n-B^n)^2+(B^n-CB^n)^2+(A^n-C^n)^2]/9