Every bet will, on average, make -1% of the amount wagered. This is true no matter what the sequence. To get the total average profit just add up all the bets and multiply by -1%.
Not quite true - if you look a few posts above I derived the expected profit for both an unbounded and a bounded martingale sequence without house edge and it's not the sum of all bets, which is what I think you're saying it would be if there was no house edge.
Your derivation suffered from an off-by-one (fencepost) error. The expected return from a game with zero house edge is zero however you play.