I can't seem to understand a lot of summation identities/manipulation. For instance, in pic related, why can't we just keep the subscripts and the lower limit equal to 'k' on the RHS? This isn't the only one, of course. Most times I see some summation proof, there's a kind of manipulation to the sum occurring that I just can't seem to understand. There's a few I understand such as index shifts, taking out a constant, splitting a sum, and a few more. Also, I can't find much math literature or videos explaining these identities that allow us to do these manipulations. Am I brainlet or is everyone else a genius? Can someone point me to a good resource for this?