# Problem Sheet - Analysis I MT22, III

> Source: https://ollybritton.com/notes/uni/prelims/mt22/analysis-i/problem-sheets/3/ · Updated: 2023-01-02 · Tags: uni, problem-sheet

What is $\overline{c}$, $\overline{c}^2 + \overline{c}$, $(\overline{c}^2 + \overline{c})^2 + \overline{c}^2$, etc. equivalent to because of conjugation rules?::
$$
\overline{c}, \overline{c^2}, \overline{(c^2 + c)^2 + c}
$$

Example question: Show that $\frac{1}{n(n-\pi)}$ converges to $0$. How would you start your rough work, and then how would you lay out your solution?::
- Rough work: Solve $|\frac{1}{n(n-\pi)}| < \epsilon$
- Solution: “Fix any $\epsilon > 0$. Set $N = \ldots$. Then, for any $n > N$…”

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