Daily Maths Challenges

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Share your cool maths problems.

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Post your solution in comments, if it is exactly the same as OP's solution, let us know.
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Post a challenge:

Doesn't have to be original, as long as it is not a duplicate.
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submitted 10 months ago by siriusmart to c/dailymaths

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Prove that the sum of the reciprocals of the Fibonacci numbers up to infinity converges to a finite value.