can someone please explain how the last line is arrived at.

I visually noticed (no math at all) that the a's on the left suddenly became (b-1)'s on the right. Everything else stayed exactly the same except for a starting at a and b starting at 1.

Hmm, it seems to me that maybe they are saying that a=b-1.
Now for a to equal 0, b must be 1. So yes, if a starts with 0, then b starts at 1
 
Please redo the derivation using pencil/paper - and I am sure you'll see how it is derived. Exactly where are you getting lost? Which term does not make sense?
I'm confused with how they concluded that mean of Y is λ(second series) and thus the mean of Y is λ.
 
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