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{\bf \Large Math 112 Homework 5}\medskip

Due Thursday March 14, 2019, on Canvas.
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You are encouraged to discuss the homework problems with 
other students. However, what you hand in should reflect your 
own understanding of the material. You are NOT allowed to copy solutions 
from other students or other sources. {\it No late homeworks will be 
accepted.}

Please pay attention to the clarity and precision of your answers. Your
solutions to the problems should always consist of carefully written 
mathematical arguments. 

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{\bf Material covered:} Rudin pages 59--72. (Problems 1 and 3 only use
Tuesday 3/5 material).
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{\bf Problem 1.} (3 points) Rudin Chapter 3 Problem 7. (Hint: consider the
quantity $(\sqrt{a_n}-\frac{1}{n})^2$).
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{\bf Problem 2.} (4 points) Rudin Chapter 3 Problem 9.
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{\bf Problem 3.} (10 points: 3,3,2,2) Rudin Chapter 3 Problem 11.

{\it Hint:} For (a), obtain a lower bound for $\frac{a_n}{1+a_n}$ by 
considering separately the cases $a_n\le 1$ and $a_n\ge 1$; be careful
in your argument! For (b),
observe that the divergence of $\sum a_n$ means that $s_n\to +\infty$. 

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