Niz
zadan je rekurzivno sa:
i
za
. Neka je
Izračunajte 
.
The sequence
is defined recursively as follows:
,
, and
for
. Let
Calculate the value of .
[lang=hr]
Niz $\{a_n\}$ zadan je rekurzivno sa: $a_0=1, a_1=2024$ i $a_{n+2}=2a_{n+1}+a_n$ za $n \ge 1$. Neka je
$$S = \sum_{i=1}^\infty \frac{a_{i-1}}{{a_i}^2 - {a_{i-1}}^2}$$
Izračunajte $S$ .
[/lang]
[lang=en]
The sequence ${a_n}$ is defined recursively as follows: $a_0=1$, $a_1=2024$, and $a_{n+2}=2a_{n+1}+a_n$ for $n \ge 1$. Let
$$S = \sum_{i=1}^\infty \frac{a_{i-1}}{{a_i}^2 - {a_{i-1}}^2}$$
Calculate the value of $S$.
[/lang]
