I can see some differences: for any finite N > 0, it's false that the sum of the first N terms of S2 is the same as the sum of the first N terms of S1. And what do we know about the infinite sum? Maybe you're right, but you'd have to prove it; they are definitely not equal "by definition"!
I can see some differences: for any finite N > 0, it's false that the sum of the first N terms of S2 is the same as the sum of the first N terms of S1. And what do we know about the infinite sum? Maybe you're right, but you'd have to prove it; they are definitely not equal "by definition"!