Proširimo Fibonaccijev niz i na negativne brojeve. Definirajmo
Izračunaj beskonačnu sumu
Let's extend the Fibonacci sequence to include negative numbers. Let's define
Calculate the following infinite sum
[lang=hr]
Proširimo Fibonaccijev niz i na negativne brojeve. Definirajmo
$$F_{-n}=(-1)^{n+1}F_n$$
Izračunaj beskonačnu sumu
$$S=\sum_{n \in \mathbb{Z}} arctan(\frac{1}{F_{3n-1}})$$
[/lang]
[lang=en]
Let's extend the Fibonacci sequence to include negative numbers. Let's define
$$F_{-n}=(-1)^{n+1}F_n$$
Calculate the following infinite sum
$$S=\sum_{n \in \mathbb{Z}} arctan(\frac{1}{F_{3n-1}})$$
[/lang]
