What is the sum of all the reciprocals of all the Fibonacci numbers?

That is, what is 1/1 + 1/1 + 1/2 + 1/3 + 1/5 + 1/8 + 1/13 + 1/21 + ... ?





I added 37 terms in the series and I got 3.359885599...





But is there an exact answer?What is the sum of all the reciprocals of all the Fibonacci numbers?
Yes, but it is known to be irrational and we don't know a closed form expression for it.


http://en.wikipedia.org/wiki/Reciprocal_鈥?/a>What is the sum of all the reciprocals of all the Fibonacci numbers?
There is... but it's irrational. About 3.35988566

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