Hello!

I just want to be sure if I did solve the task correctly.

The task is:

Prove that bn is odd for integers n>=1

for k>=3

The attempt at a solution

Induction basis:

true 1 is odd

true 2 is odd

Now the question is:

Could I use the strong (complete) induction?

If I can use it, the solution is simple:

Let the recurrence relation is true for all k, such that n<k and n=k i.e n<=k

then for n=k+1

is odd and is even therefore odd+even=odd

Is this correct?

Thank you.

Regards.