Proof that the rth term can be found by finding the difference between the sum of the first r terms and the sum of the first (r-1) terms: That is, .
What I really don't understand is . For example, what is the of ? Is it ? Or ?
Yeah. I see. But how on Earth would you come up with that first? I mean, say you wanted to come up with this formula for the rth term, and you don't know that it's ? What we did now there was to confirm that . There is no way I could have simply thought: Ah, find the difference between the sum of the first r terms and the sum of the first (r-1) terms.