I tried proving this sequence = the formula (2n)(n+1)
n = 1 2 3 4
6 20 42 72
multiple ways. Initially using Arithmetic sequences with a second difference, and Geometric sequences which just didn't make much sense. Now i'm just completely out of ways to prove it.
I already know the formula which achieves these numbers, (2n)(n+1), but i cannot prove coherently that this is the correct solution. My question being, how do I solve this, and how do I prove it works?
n = 1 2 3 4
6 20 42 72
multiple ways. Initially using Arithmetic sequences with a second difference, and Geometric sequences which just didn't make much sense. Now i'm just completely out of ways to prove it.
I already know the formula which achieves these numbers, (2n)(n+1), but i cannot prove coherently that this is the correct solution. My question being, how do I solve this, and how do I prove it works?