The reason why he did that is more apparent when you take the limit as n approaches infinity. As you approach infinity with n, your number of terms approach infinity, additionally, the nth term is changing with the number of terms. In order to deal with all these extra terms you have to do something akin to what he does here. Think of Lim as n approaches infinity of a simple geometric series like (1 + 2 +4 +8 + ... 2^k)
You need to explain why you decide to make steps like multiplying S by α and then subtracting.
The reason why he did that is more apparent when you take the limit as n approaches infinity. As you approach infinity with n, your number of terms approach infinity, additionally, the nth term is changing with the number of terms. In order to deal with all these extra terms you have to do something akin to what he does here. Think of Lim as n approaches infinity of a simple geometric series like (1 + 2 +4 +8 + ... 2^k)
This video needs more thorough explanation.
This was very helpful thank you.
still confused