The sum of the first n Fibonacci numbers with odd indices

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Health & Science mathematics fibonacci numbers fibonacci identity sum

Episode 24.

The sum of the first n Fibonacci numbers with odd indices.
Theorem. The sum of the first n Fibonacci numbers with odd indices is equal to the 2n-th Fibonacci number. $f_1+f_3+f_5+\ldots+f_{2n-1}-f_{2n}$.

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