# Analytical Fibonacci

We derive Binet’s equation for the n^{th} Fibonacci number as

- 13 August, 2012 -
- Article, Math Problems -
- Tags : algebra, analysis, titu
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Using the method derived in the previous article, we first solve the characteristic polynomial associated with the linear recurrence

described by

Via the quadratic equation, we see that the solution to gives solutions .

Therefore, the coefficients of are

therefore giving .