Daily Assignment for Friday, March 21

Due Monday, March 31 on Canvas.

• Read §§9.2 and 9.3.
• Optional exercise : In class, we computed \( \zeta(2) = \sum_{n=1}^\infty \frac1{n^2} \) to be \( \frac{\pi^2}{6} \). Use the same method to compute \( \zeta(4) = \sum_{n=1}^\infty \frac1{n^4} \).
• Optional exercise : In class, we met \( \Gamma(s) = \int_0^\infty t^{s-1} e^{-t} dt \). Compute \( \Gamma(1) \) and then use integration by parts to compute \( \Gamma(n+1) = n \Gamma(n) \). Conclude that \( \Gamma(n) = (n-1)! \) when \( n \) is a positive integer.
• Assign yourself a grade for this assignment :
  1. At least 60 minutes.
  2. About 45 minutes.
  3. About 30 minutes.
  4. About 15 minutes.
  Submit your grade as a submission comment with your assignment. This comment must be the first comment and it must be exactly 1 character long or the grade won't be registered.