Hey, I have some questions from my Differential class that I am really confused on. I still don't completely understand Fourier, but I really don't understand this. I don't want the answers, just someone to explain how to go about doing these. Thanks!

Problem 1

Let $\displaystyle f(t)=t^2$ for $\displaystyle 0<t<2$ and suppose $\displaystyle f(t+2)=f(t)$ for all $\displaystyle t \epsilon R-2Z$. By $\displaystyle 2Z$, we denote even integers. Define $\displaystyle f(2k)=1$ for $\displaystyle k \epsilon Z$. Calculate the Fourier Series for $\displaystyle f$.

Problem 2

Show, by the result of the last problem, $\displaystyle \sum_{n=1}^\infty \frac{\sin{nt}}{n}=\frac{\pi-t}{2}$. Derive a series which converges to $\displaystyle \pi$ by setting $\displaystyle t$ to a particular value and doing a little algebra. How many terms in this series would you have to sum in order to obtain the digits 3.14 in $\displaystyle \pi$ with certainty?