I hate Rudin’s book on mathematical analysis that is supposedly used in all– well, most– undergrad courses in real analysis. It is horrible reading: one theorem after another, with no connective tissue. Some– most– reviewers on Amazon.com say that is laudible conciseness. Personally, I think that it is overly terse… and I would say I have had more exposure to the ideas in Rudin than most people in my class, yet the book manages to bore and confuse me at the same time.

Anyhow, here’s one good problem from Rudin: Given the sequence defined as
, , show that converges, and that it is bounded above by 2.

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