The sum of the first n Fibonacci numbers with even indices

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Health & Science mathematics fibonacci fibonacci numbers identity sum

Episode 28.

The sum of the first n Fibonacci numbers with even indices.
Theorem. The sum of the first n Fibonacci numbers with even indices is equal to the (2n+1)-th Fibonacci number minus 1. $f_2+f_4+f_5+\ldots+f_{2n}=f_{2n+1}-1$.

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