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A Baby Rudin Related Question

See the attachment for my question.

I am confused on how to do this problem... I need a little bit of help getting started.

(a), (b), and (c) seem trivial. I can't think of doing anything other than actually going through this process a couple of times to show these are all true by induction. I however have no idea nor understand part (d). Parts (e) and (f) I think I can manage pretty easily after getting the others done. Do you guys think induction is appropriate for the first 3? and could someone help shed some light on part (d).

This whole problem seems pretty weird to me. I dont even see how you could pick a pair of to start with..