add pi^2/6 problem

1 files changed, 3 insertions, 0 deletions

diff --git a/Problem Set 3.page b/Problem Set 3.page
index b1011b9..9504969 100644
--- a/Problem Set 3.page
+++ b/Problem Set 3.page
@@ -43,4 +43,7 @@ $$ f(z + 2\pi) = f(z) $$
 $$ f(z + \tau) = f(z) $$
 (Such a function is said to be doubly periodic).  Show that $f$ is constant.  Hint: Write down holomorphic Fourier series for $f(z)$ and $f(z+\tau)$, and compare their Fourier coefficients.
 
+11. Compute the Fourier coefficients of the function $f(x) = \frac{1}{2} - \frac{x}{\pi}$ and use this to show that
+$$ \sum_{n = 1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6} $$
+
 # Solutions