Mladi matematičari se jako dobro zabavljaju na ovom partyju, a
Fibonacci nastavlja dalje sa svojim trikovima. Za svoj sljedeći zadatak
Fibonacci je rekao matematičarima da će morati malo zbrajati,a pod malo je mislio beskonačno brojeva jer sljedeći zadatak glasi
Izračunaj beskonačnu sumu 
.
Ako je rješenje razlomak zapiši ga u obliku 
gdje je 
brojnik, a 
nazivnik potpuno skraćenog razlomka.
The young mathematicians are having a ton of fun at the party and
Fibonacci is pulling out new problems out of his hat. For the next trick he needed a volunteer. After he found one,
Fibonacci told them that they will have to do just a bit of addition, and by a bit he meant infinitely many times because this task was:
Find the result of the infinite sum .
If the solution is a fraction, write it like you did in the previous task.
[lang=hr]
Mladi matematičari se jako dobro zabavljaju na ovom partyju, a \emph{Fibonacci} nastavlja dalje sa svojim trikovima. Za svoj sljedeći zadatak \emph{Fibonacci} je rekao matematičarima da će morati malo zbrajati,a pod malo je mislio beskonačno brojeva jer sljedeći zadatak glasi
Izračunaj beskonačnu sumu $$\sum^\infty_{n=2} \frac{1}{F_{n-1}F_{n+1}} $$.
Ako je rješenje razlomak zapiši ga u obliku $a/b$ gdje je $a$ brojnik, a $b$ nazivnik potpuno skraćenog razlomka.
[/lang]
[lang=en]
The young mathematicians are having a ton of fun at the party and \emph{Fibonacci} is pulling out new problems out of his hat. For the next trick he needed a volunteer. After he found one, \emph{Fibonacci} told them that they will have to do just a bit of addition, and by a bit he meant infinitely many times because this task was:
Find the result of the infinite sum $$\sum^\infty_{n=2} \frac{1}{F_{n-1}F_{n+1}} $$.
If the solution is a fraction, write it like you did in the previous task.
[/lang]
