Dror Bar-Natan: Classes: 2002-03: Math 157 - Analysis I: | (242) |
Next: Eric DeGiuli's Solution of Homework Assignment 22
Previous: Class Notes for the Week of March 3 (6 of 6) |

Assigned Tuesday March 11; due Friday March 21, 2PM at SS 1071

this document in PDF: HW22.pdf

**Required reading. ** All of Spivak Chapter 23. Also read (but
don't do!) all exercises for that chapter -- just to get an impression for
how intricate the various convergence tests and criteria can get.

**To be handed in. ** From Spivak Chapter 23: 1 (parts divisible
by 4), 12, 23 as well as the following question:

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

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

- 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).

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

Dror Bar-Natan 2003-03-11