Niz
je zadan uvjetima
Odredite zbroj
. Ako je zbroj
, gdje su
i
relativno prosti, rješenje zapišite tako što uzastopno bez razmaka zapišete
i
.
The sequence
is given with
Find
. If it is equal to
, where
and
are coprime, write the solution by writing
and
consecutively, without spaces.
[lang=hr]
Niz $(a_n)$ je zadan uvjetima
\[
a_1 = \frac{1}{2} \quad \text{i} \quad a_m = \frac{a_{m-1}}{2m a_{m-1} + 1} \quad \text{za } m > 1.
\]
Odredite zbroj $a_1 + a_2 + \dots + a_{2026}$. Ako je zbroj $\frac{a}{b}$, gdje su $a$ i $b$ relativno prosti, rješenje zapišite tako što uzastopno bez razmaka zapišete $a$ i $b$.
[/lang]
[lang=en]
The sequence $(a_n)$ is given with
\[
a_1 = \frac{1}{2} \quad \text{and} \quad a_m = \frac{a_{m-1}}{2m a_{m-1} + 1} \quad \text{for } m > 1.
\]
Find $a_1 + a_2 + \dots + a_{2026}$. If it is equal to $\frac{a}{b}$, where $a$ and $b$ are coprime, write the solution by writing $a$ and $b$ consecutively, without spaces.
[/lang]
