you can use the fact that and . This will allow you to set up an induction step.
The Fibonacci Numbers : 1,1,2,3,5,8,13,21,34... are defined by and for n >2 by .
Show by induction that is even.
base case: n=3 is 2, so it is even.
Assume is even?
not sure how to do the induction step.
Thanks in advance
This is because the first 2 terms are odd
The sequence cycles in this way
The inductive step is..... does being even cause to be even ?
If is even, then both and must of necessity both be odd.
Hence, as this is true, and is even, is even.
The inductive proof is really just basic logic in this case!