Some Sums Related to Sums of Oresme Numbers

Abstract

In [1] A. F. Horadam presented a history of number attributed to Nicole Oresme, namely the sequence

$$ \{ {O_n}\} = \{ \frac{n}{{{2^n}}}\} = \{ \frac{1}{2},\frac{2}{4},\frac{3}{8}, \ldots ,\frac{n}{{{2^n}}}, \ldots \} $$

((1.1))

.