Solution for Exercise 06 from Chapter 03 in Baby Rudin

[ceciliachan1979]

This pull request provides the solution for Exercise 06, Chapter 03, from the third edition of Principles of Mathematical Analysis by Walter Rudin.

[E7-87-83]

(a) ok.

(b) by Theorem 3.28, sum 1/sqrt(n) diverges. 但用Comparsion test嘅方向係岩嘅, hint: prove sqrt(n+1) - sqrt(n) < 1/(2 sqrt(n))

(c) ok

(d) ok for the written. Hint: For any complex number a,b, |a+b| =< |a|+|b|.

[E7-87-83]

(d) \frac{|z^n|-1}{|z^{n+1}|-1} > \frac{|z^n|-1}{|z^{n+1}|}
for example, z=2, n=1, 1/3 > 1/4

[E7-87-83]

Part (d) |z| > 1 ok.

For |z| <= 1 [P.S. solution裏打錯sign], Rudin comparison test 喺證明 diverges 方面，無包括complex numbers 嘅cases.

[ceciliachan1979]

Rudin comparison test 喺證明 diverges 方面，無包括complex numbers 嘅cases.

Good observation，冇留意到，呢個位值得諗一諗。