iran-konkur 2014 Q105

iran-konkur · Other · konkur-riazi_1393 Sequences and series, recurrence and convergence Summation of sequence terms
105- What is the value of $\dfrac{t^{11}+t^{10}+t^9+\cdots+t+1}{t^4+t^2+t^2+1}$, for $t=\dfrac{-1+\sqrt{5}}{2}$?
(1) $2$ (2) $3$ (3) $4$ (4) $5$
\textbf{105-} What is the value of $\dfrac{t^{11}+t^{10}+t^9+\cdots+t+1}{t^4+t^2+t^2+1}$, for $t=\dfrac{-1+\sqrt{5}}{2}$?

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(1) $2$ \hfill (2) $3$ \hfill (3) $4$ \hfill (4) $5$

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