Mock AIME 4 2006-2007 Problems/Problem 13
can be written in the form , where . Compute the remainder when is divided by 100.
First let us develop a formula for sums of arctans. Let us say we want to find , so we take the tangent of that and you get:
, now if we take the arctan of both sides we get:
If we say that , then we get
Therefore the sum telescopes leaving us with and
i don't know if my answer is right as there is no answer key for this test.