1 / F(1)*F(3) + 1 / F(3)*F(5) + ... + 1 / F(2*n+1)*F(2*n+3) ---> phi^(-1) ? (Fibonacci #)

[lvl107]

Hello, Everyone.

From testing :

Thanks in advance.

[Werner_E · Accepted solution]

Fibonacci - so many formulas, so few time ...

Given that its not a Mathcad questions and probably also can't be done/proven with Mathcad, I guess chances are rather low that anyone will present a formal proof here.

Maybe you find here

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibFormulae.html

and/or in the reference section at the end something of interest.

Maybe you are especially interested at Vajda

https://www.amazon.com/exec/obidos/ASIN/0486462765/fibonacnumbersan

or Johnson

www.maths.dur.ac.uk/~dma0rcj/PED/fib.pdf

[lvl107]

   Many thanks for your time and help, Werner. 

       Regards.

[lvl107]

  Hello, Everyone again.

  I think my question should be : "Need help having a proof of "

   Thanks in advance.

[lvl107]

   and a equivalent question is :

  Thanks in advance.