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- ...his means proving first that the result holds for <math>n=1</math> (in the Base Case), and then proving that having the result hold for <math>{n=k}</math> ...tead of all of them; in this case, you would take <math>n=2</math> as your base case, and show that if <math>{n=k}</math> gives the desired result, so does5 KB (768 words) - 23:59, 28 September 2024
- ...[phinary]], which is base [[phi]]; others include "[[Fibonacci base]]" and base negative two. [[Binary]] is base 2. It's a favorite among computer programmers. It has just two digits: <ma2 KB (351 words) - 09:39, 1 October 2015
- === Fibonacci numbers === ...\frac{n}{2}\right \rfloor} = F(n+1)</math>, where <math>F(n)</math> is the Fibonacci sequence. For example, <math>{6 \choose 0}+{5 \choose 1}+{4 \choose 2}+{35 KB (838 words) - 16:20, 3 January 2023
- ...ten digits is the last to appear in the units position of a number in the Fibonacci sequence? ...he integers on the winning ticket have the same property— the sum of the base-ten logarithms is an integer. What is the probability that Professor Gamble13 KB (1,948 words) - 09:35, 16 June 2024
- ...ath>(111)_B=(aabbcc)_6</math>, where <math>a,b,c</math> represent distinct base <math>6</math> digits, <math>a\neq 0</math>. 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
- ...hat in general <math>\{s_n\}</math> is the set of the first <math>n</math> Fibonacci numbers. To show this note that if <math>\{s_n\} = \{F_0, F_1, ... F_n\}</m ...tion is satisfied is <math>n=13</math> and the exponential behavior of the Fibonacci numbers ensure that every <math>n</math> greater than <math>13</math> will5 KB (930 words) - 01:17, 7 March 2018
- In 1989, L. Ming showed that there are only 4 distinct numbers which are both Fibonacci numbers and triangular ...which satisfies the property that it is equal to the sum of the digits (in base ten) of its cube?14 KB (2,904 words) - 17:24, 16 May 2017
- ...ibilities. Thus, by induction, <math>f(n)</math> is the <math>n+1</math>th Fibonacci number. ...+ a_{n-2} + F_{n-2}.</math> (The <math>F_i</math> is the <math>i</math>th Fibonacci number). From here, we can construct a table of the values of <math>a_n</ma15 KB (2,414 words) - 21:00, 30 July 2024
- Let's begin by drawing a triangle that starts at the origin. Assume that the base of the triangle goes to the point <math>x = 1</math>. The line <math>x = y< ...r phi (<math>\phi</math>). Phi has many properties and is related to the [[Fibonacci sequence]]. See [[Phi]].14 KB (2,223 words) - 13:27, 1 September 2024
- ...is motivation to turn this closed formula into a recurrence relation. The base of the exponents are the roots of the characteristic equation <math>r^3-1=05 KB (886 words) - 22:57, 1 November 2024
- ...many digits does this number of dollars have when written as a numeral in base <math>5</math>? (The approximation of <math>\log_{10} 5</math> as <math>0.7 The Fibonacci numbers are defined by <math>F_1=1,</math> <math>F_2=1,</math> and <math>F_14 KB (2,186 words) - 11:30, 15 November 2024