How do you determine how many cases to consider in base case of strong induction?

1. I'm trying to learn to strong induction and I'm beginning understand the steps. However I can't seem to understand why some examples have multiple base cases. What do you look for while choosing base cases?

2. I read it almost everywhere that strong induction and weak induction are variants and that what can be proved with one can be proved with another. I just need a favor, can someone show me how to prove 1+2+3+...+n=n(n+1)21+2+3+...+n=n(n+1)2 using strong induction? I need to compare the two so I can understand strong induction a little better.

Thank you very much, my syllabus includes weak and strong induction both. But my textbook has merely just mentioned the definition of strong induction and all the solved examples are solved using weak induction.