© | Dror Bar-Natan: Classes: 2004-05: Math 157 - Analysis I: | (103) |
Next: Class Notes for Tuesday March 22, 2005
Previous: Solution of Term Exam 4 |

Assigned Tuesday March 22; due Friday April 1, 2PM,
at SS 1071

this document in PDF: HW.pdf

**Required reading. ** All of Spivak's Chapters 22
and 23.

**To be handed in. ** From Spivak Chapter 23:
Problems 1 (parts divisible by 4), 12, 23.

**Recommended for extra practice. ** From Spivak
Chapter 23: Problems 1 (the rest), 5, 20, 21.

**In class review problem(s)** (to be solved in
class on Thursday March 31):

- Prove that the following sums diverge: (Hint: Use problem 20.)
- Prove that the following sums converge: (Hint: Use problem 20.)

**Just for fun. **
In this question we always assume that and .
Let's say that a sequence is ``much bigger'' than a sequence
if
. Likewise let's say that a
sequence is ``much smaller'' than a sequence if
. Prove that for every convergent series
there is a much bigger sequence for which is
also convergent, and that for every divergent series there is
a much smaller sequence for which is also divergent. (Thus
you can forever search in vain for that fine line between good and evil; it
just isn't there).

**Advertisement 1'. ** A short addendum to
Advertisement 1 of HW21:

Date: Sun, 20 Mar 2005 21:53:48 -0500 Dr. Bar-Natan: Thank you for posting our announcement on your website, the advertising is greatly appreciated! However, a minor note: technically, this event *does* include free food - 5 meals (not to mention a T-shirt!) are included in the $60 registration fee, truly a fantastic bargain! ;) Cheers, Erica Blom

The generation of this document was assisted by
L^{A}TEX2`HTML`.

Dror Bar-Natan 2005-03-21