Fibonacci sequence

Definition

In mathematics, the Fibonacci sequence is a sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted Fn . The initial elements of the sequence are F1 = 1 and F2 = 1, though many authors also include a zeroth element F0 = 0. Starting from F0, the sequence begins0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...

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1/2 + 1/4 + 1/8 + 1/16 + ⋯1/2 − 1/4 + 1/8 − 1/16 + ⋯1/4 + 1/16 + 1/64 + 1/256 + ⋯1 + 1 + 1 + 1 + ⋯1 + 2 + 3 + 4 + ⋯1 + 2 + 4 + 8 + ⋯1 − 1 + 2 − 6 + 24 − 120 + ⋯1 − 2 + 3 − 4 + ⋯1 − 2 + 4 − 8 + ⋯8SVX AVL tree Abraham de Moivre Absolute convergence Abundant number Achilles number Additive persistence Agile management Alexander Braun Aliquot sequence Almost perfect number Almost prime Alternating series Amenable number Amicable numbers Amiga Analysis of algorithms Angle Arbitrarily large Arbitrary-precision arithmetic Aristid Lindenmayer Arithmetic dynamics Arithmetic function Arithmetic number Arithmetic progression Aronson's sequence Artichoke Asymptotic analysis Automorphic number BBC Ban number Bee Bell number Betrothed numbers Bharata Muni Bijection Binary number Binary numeral system Binary tree Binet's formula Binomial coefficient Biology Bit Blum integer Cake number Canadian Mathematical Bulletin Cardinality Carmichael's theorem Carmichael number Cassini's identity Cassini and Catalan identities Catalan number Catalan pseudoprime Cauchy sequence Centered cube number Centered decagonal number Centered dodecahedral number Centered heptagonal number Centered hexagonal number Centered icosahedral number Centered nonagonal number Centered octagonal number Centered octahedral number Centered pentagonal number Centered polygonal number Centered polyhedral number Centered square number Centered tetrahedral number Centered triangular number Circle packing theorem Circular arc Closed-form expression Coefficient Colossally abundant number Combinatorial proof Companding Complete sequence Complex number Composite number Composition (combinatorics)Comptes rendus de l'Académie des Sciences Conditional convergence Conformal map Congruent number Conjecture Conjugate (square roots)Continued fraction Convergent (continued fraction)Convergent sequence Convergent series Conversion of units Coprime integers Cube (algebra)Cullen number Cycle detection Cyclic number Cyclic number (group theory)Daniel Bernoulli Data structure Decagonal number Dedekind number Deficient number Delannoy number Derivative Descartes number Determinant Difference equation Digit-reassembly number Digit sum Digital root Diophantine equation Dirichlet series Divergence of the sum of the reciprocals of the primes Divergent series Divisibility sequence Divisor Divisor function Dodecagonal number Dodecahedral number Domino tiling Donald Knuth Double Mersenne number Drone (bee)Dudeney number Economics Edmund Landau Edsger W. 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