Induction Recursive
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A sequence $T_n$ is defined such that
\[T_k = T_{k-1}+T_{k-2} \text{ and } T_1 = 1,\, T_2 = 1 \qquad (k\geq 3)\]
Use the method of mathematical induction to show that:
\[T_n = \frac{1}{\sqrt{5}}\left\{\left(\frac{1+\sqrt{5}}{2}\right)^n-\left(\frac{1-\sqrt{5}}{2}\right)^n\right\}\]
\((T_n \text{ is the } n\text{th fibonacci number})\)
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