2006 GCTM State Tournament Problems/Individual Problem 46
Revision as of 14:22, 7 August 2006 by Boy Soprano II (talk | contribs)
Problem
Find the exact value of the infinite series .
Solution
Motivated by the formula for the subtraction of cotangents, we observe that
Thus
,
which is a telescoping series equal to . We note that
, so our infinite sum is equal to
, which is equal to
. Q.E.D.