Difference between revisions of "AoPS Wiki talk:Problem of the Day/September 5, 2011"
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Latest revision as of 08:28, 7 September 2011
Problem
Simplify
Solution
The series
is a geometric series, which famously converges to 2. This can by applying the formula for infinite geometric sums,
where
is the first term and
is the ratio. For this series, the sum is
. Thus, since the problem asks for twice this number, the answer is
.