HW2, due Monday Sep12

  • Problem 1, page 26 (add details to the brief sketch of this that was made in class).
  • Problem 9, page 27.
  • Problem 17, page 27.
  • Problem 20, page 27.
  • Problem 25, page 27.  (You will receive full credit for showing the formal identity when s=2.  By “formal identity” it means that you do not need to prove convergence.  Hint: look at the first few lines of the proof of Theorem 3, which does the case s=1 (which was also covered in class on Sep7 ). Adapt the argument to s=2.  When s=2 the series is 1 + 1/2^2 + 1/3^2 + 1/4^2 + …  Can you find a way to “factor” this using prime factorization in the same way we factored 1 + 1/2 + 1/3 + 1/4 + … in class on Wednesday?
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