 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2015/discrete-mathematics-continuous-mathematics-and-probability-resit/6/a/iv/solution

x = 1

, the left limit is

1

. The right limit is

- 1

because of the period-two extension. Therefore Dirichlet's theorem on Fourier series gives the Fourier series limit

\frac{f ( 1 ^{-} ) + f ( 1 ^{+} )}{2} = \frac{1 - 1}{2} = 0.

Every Fourier partial sum is also exactly zero there because

sin ((2 j + 1) π) = 0

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