F furnz New Member Joined Jul 25, 2006 Messages 9 Gender Male HSC 1999 Dec 13, 2009 #1 Can someone help me out with the K+1 steps on this question please Prove 12^k >= 5^k + 7^k Thanks
I Iruka Member Joined Jan 25, 2006 Messages 544 Gender Undisclosed HSC N/A Dec 13, 2009 #2 The thing to note is that 12 is bigger than either 5 or 7. Thus 12^(k+1)=12.12^k >=12.5^k+12.7^k (by the inductive hypothesis) > 5.5^k + 7.7^k = 5^(k+1)+7^(k+1) as required.
The thing to note is that 12 is bigger than either 5 or 7. Thus 12^(k+1)=12.12^k >=12.5^k+12.7^k (by the inductive hypothesis) > 5.5^k + 7.7^k = 5^(k+1)+7^(k+1) as required.
