Problem Sheet - Analysis I MT22, III
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 $ \vert \frac{1}{n(n-\pi)} \vert < \epsilon$
- Solution: “Fix any $\epsilon > 0$. Set $N = \ldots$. Then, for any $n > N$…”