Sorry! I realised I left out some details!

Let $\displaystyle t_{j}=j/100, a_{j}=j,b_{j}=-j$ for $\displaystyle j=0,...,99$. Define

$\displaystyle f(t)= \sum_{k=0}^{99}(a_{k}\textup{cos}(2\pi{kt})+b_{k}{ sin}(2\pi{kt}))$

.

Define $\displaystyle f(t_{j})$ by $\displaystyle x_{j}$ for $\displaystyle j=0,...,99.$Determine the values of $\displaystyle c_{l},d_{m}$ for $\displaystyle l=0,...,5,m=1,...,4$, so that

$\displaystyle P(t)=c_{0}+\sum_{k=1}^{4}(c_{k}\textup{cos}(2\pi{k t})+d_{k}\textup{sin}(2\pi{kt}))+c_{5}\textup{cos} (10\pi{t})$

is the least squares approximation to the data points $\displaystyle (t_j,x_j)$ for $\displaystyle j=0,...,99$.