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- ...In other words, if you divide the <math>n^th</math> term of the Fibonacci series over the <math>(n-1)^th</math> term, the result approaches <math>\phi</math2 KB (293 words) - 20:12, 14 February 2025
- Compute the sum of all twenty-one terms of the geometric series Let <math>T=\text{TNFTPP}</math>. Three distinct positive Fibonacci numbers, all greater than <math>T</math>, are in arithmetic progression. Le30 KB (4,794 words) - 22:00, 8 May 2024
- ...xplicit, closed form formula used to find the <math>n</math>th term of the Fibonacci sequence. If <math>F_n</math> is the <math>n</math>th [[Fibonacci number]], then6 KB (955 words) - 01:11, 5 February 2025
- And there is the repetition. So, this series has a period of 24. <math>2009 \equiv 17 \pmod{24}</math>, so <math>|a_{200 ...meaning <math>a_3 = \tan{75}</math>. So, the sequence becomes a sort of [[Fibonacci sequence]] with angle measures. We continue to sum angle measures, like so7 KB (994 words) - 15:57, 9 July 2024
- For example, let <math>F_n</math> be the <math>n</math>th [[Fibonacci number]] defined by <math>F_1 = F_2 = 1</math>, and ...oblems]] below to see an example of how to do this. In particular, for the Fibonacci numbers, this yields [[Binet's formula]]. <br><br>19 KB (3,412 words) - 13:57, 21 September 2022
- geometric series: http://mahalanobis.twoday.net/stories/3472911/ Fibonacci: sum_{i=1}^{2n-1} F_iF_{i+1} = F_{2n}^255 KB (7,998 words) - 15:07, 16 September 2024
- ...ath>5</math> and the numerators <math>1, 1, 2, 3, 5, \ldots</math> are the Fibonacci numbers (a): Knowing that the formula for an infinite geometric series is <math>A/(1 - r)</math>, where <math>A</math> and <math>r</math> are the1 KB (156 words) - 04:26, 12 January 2019
- The Fibonacci numbers are defined by <math>F_1 = 1, F_2 = 1,</math> and <math>F_n = F_{n- Plug in a few numbers to see if there is a pattern. List out a few Fibonacci numbers, and then try them on the equation. You'll find that <math>{\frac{F5 KB (834 words) - 22:37, 1 January 2025
- 2.Show that the series 3. Let <math>F_n</math> denote the <math>n</math>th Fibonacci number. Prove that if <math>n</math> is odd, then all odd prime divisors of64 KB (10,564 words) - 21:17, 19 February 2025