Pisano Period - Sums

Sums

Using

F(0) + F(1) + F(2) + … + F(k) = F(k + 2) − 1,

it follows that the sum of π(n) consecutive Fibonacci numbers is a multiple of n.

Moreover, for the values in the table the sum of π(n) consecutive Fibonacci numbers is n times the (π(n)/2 + 1)th element:

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