  In this paper, we study the theory of the harmonic and the hyperharmonic
Fibonacci numbers. Also, we get some combinatoric identities like as harmonic
and hyperharmonic numbers and we obtain some useful formulas for
$\mathbb{F}_{n}$, which is finite sums of reciprocals of Fibonacci numbers. We
obtain spectral and Euclidean norms of circulant matrices involving harmonic
and hyperharmonic Fibonacci numbers.
