I posted a bit about the characteristic value of a Fibonacci series without proof but nowI wonder about whether it could be valid. A remarkable result of it applies to the binominal coefficients. The sum of following Binominal coefficients times corresponing Fibonacci numbers are in them selves terms from the Fibonnacci series. In other words, each of the following sums is a Fibonacci number. "(n,i)" is used her to represent the the binominal coefficients(adsbygoogle = window.adsbygoogle || []).push({});

A. [tex]\sum_{i=0}^{n}F_{i-1}(n,i)[/tex]

B. [tex]\sum_{i=0}^{n}F_{i-2}(n,i)[/tex]

For intance;

[tex]F_{-1}*1 + F_{0}* 3 + F_{1}*3 + F_{2}*1 = F_{5}[/tex]

[tex]F_{-2}*1 + F_{-1}*3 + F_{0}*3 + F_{1}*1 = F_{4}[/tex]

[tex]F_{-1}*1 + F_{0}*4 + F{1}*6 + F_{2}*4 + F_{3}*1 = F_{7}[/tex]

I could go on but that in it self does not prove the result.

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# How do I prove my result?

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