YannY said:
Ahaha you made that up in your head
Let me demonstarte with an example.
2005 ext1 HSC Q4d)
Prove by induction that 4^n -1 - 7n >0 for n >or= 2
Step 1: for n = 2, 16-1-14=1 >0
Step 2: Assume that
4^k-1-7k>0
Step 3: Prove that 4^(k+1) - 1 -7(k+1) >0
LHS =4.4^k - 8 - 7k
now from the assumption, 4^k>1+7k, so if we replace 4^k with (1+7k) which is smaller, then
LHS > 4(1+7k) -8-7k
>4+28k-8-7k
>21k -4 >0 as k>or=0