Math 33B/1 S00 G.

Assignment #3

Note quiz announcement below.

Homework assignment #3 is due in lecture Friday, April 21. Be sure to try these problems before your discussion section!

section	page	To do but not hand in	To hand in
§3.4	p. 119	20, 26	28, 30
§3.5	p. 125	1, 3, 5, 9, 15, 23, 29	2, 4, 6, 10, 14, 16, 18, 22, 30
§3.6	p. 129	1, 3, 5	2, 4, 8, 10, 16
below			G-1

Quiz in section, Week 3 (April 18 and 20): One problem similar in spirit to p. 119, Ex. 28. What would you do, for example, if the denominator were n^1.1 instead? Some ideas: (1) It's OK to work with a tail of the series instead of the whole series, applying some test. (2) Compare with 1/n^p where p is lower than the exponent in the problem but still larger than 1.

Problem G-1.   You know that the harmonic series diverges, so its partial sums are not bounded--they eventually pass 10, then 20, then 30, and so on. However, the harmonic series diverges very slowly. Give an estimate of how many terms are needed before the the partial sum reaches 20.

(Method: Think about the integral test, which shows that the partial sums are sort of like the integral of 1/x out further and further. But to be more accurate, use the fact about the ``Euler constant'' gamma mentioned at the end of Handout F. It says approximately how far off the partial sums are from the log function. To get your estimate, just pretend this approximation is exact. From now on you are responsible for knowing the definition of the Euler constant.)