Općinsko natjecanje 1999 SŠ4 4
Dodao/la:
arhiva2. travnja 2012. Niz
![a_1](/media/m/6/1/7/6173ac27c63013385bea9def9ff2b61e.png)
,
![a_2](/media/m/4/0/1/401f4cdfec59fba73ae32fa6769c72cb.png)
,
![\dots](/media/m/3/6/1/36118a223c1f6e75548277354fbabc8a.png)
,
![a_n](/media/m/1/f/f/1ff6f81c68b9c6fb726845c9ce762d7a.png)
,
![\dots](/media/m/3/6/1/36118a223c1f6e75548277354fbabc8a.png)
definiran je ovako:
![\begin{align*}
a_1&=1, \\
a_n&= \dfrac{n+1}{n-1}(a_1+a_2+\cdots+a_{n-1}),\quad n>1.
\end{align*}](/media/m/f/2/0/f20838a4e1b79673802b1c98918b3937.png)
Odredite
![a_{1999}](/media/m/7/1/f/71f5680c4fa06e5f1a3c9a88d5fb5f73.png)
.
%V0
Niz $a_1$, $a_2$, $\dots$, $a_n$, $\dots$ definiran je ovako: $$$\begin{align*}
a_1&=1, \\
a_n&= \dfrac{n+1}{n-1}(a_1+a_2+\cdots+a_{n-1}),\quad n>1.
\end{align*}$$$
Odredite $a_{1999}$.
Izvor: Općinsko natjecanje iz matematike 1999