I am a university student and I was self-teaching myself induction methods.
I did question (3)(b). The answer to (3)(a) is g n = 2^n + 1 for n is a positive natural number.
My solution differs from the given solution by the university.
Mine has 2 base cases. I see that the given solution has 1 base case but it splits its inductive step into two cases (while I don't).
I've taken screenshots below for quick reference.
My solution (please mind my poor handwriting):
The question is, is my solution perfectly okay -i.e. is a perfectly valid strong induction proof? Is there something I have done wrong or something I have done badly against convention.
Which solution is better or preferred - and why? (i.e. which style can be more easily applied to other questions)
Thank you in advance.