There are more questions below than what you need to hand in. You choose, which ones to hand in.

Submit for marking a total of 15 solutions to questions (not more). Of the questions that you hand in, 13 need to be analytically solved (handwritten or typeset) and 2 need to be Mathematica based questions.

Each analytic question weights 6pts/100; each Mathematica based question weighs 11pts/100.

In your hand-in, please try and order the questions in ascending order. Also, for each question please try to note both the number of the question as appearing below as well as the example number. It is best if you place the Mathematica based questions last, making sure to submit both Mathematica code and output.

1. Example 119.
2. Example 120.
3. Example 124.
4. Show that the sequence a_k = 5*2^k satisfies the recurrence relation a_n = 2*a_{n-1}.
5. Find a recurrence relation for the "Catalan Numbers" and explain the rational behind it (you may search the web).
6. Example 4 on page 65 in Section 4.2
7. Example 126. Carry out the analysis for a similar example: a_n = Sin(Log(n))/n.
8. Argue why the limit of n^(1/n) is 1.
9. Reproduce Example 128.
10. Reproduce a proof that the harmonic series diverges.
11. Example 129 with 7% interest instead of 5%.
12. Choose some of the questions from this extra set containing questions (a) -- (m) .
13. Look at the limit explained here. Reproduce these calculations explaining the steps involved.