A sequence defined by a rule from earlier terms is a recurrence. The Fibonacci numbers are the classic: each is the sum of the previous two. Many recurrences have a closed form, for Fibonacci it involves the golden ratio, but computing them term by term is often the clearest path.
Töötatud näide · fib(20)
Samm-sammult
- F_0 = 0,; F_1 = 1
Each Fibonacci number is the sum of the two before it.
- F_{2} = F_{1} + F_{0} = 1
- F_{3} = F_{2} + F_{1} = 2
- F_{4} = F_{3} + F_{2} = 3
- F_{5} = F_{4} + F_{3} = 5
- F_{6} = F_{5} + F_{4} = 8
- F_{7} = F_{6} + F_{5} = 13
- F_{8} = F_{7} + F_{6} = 21
- \vdots
- F_{19} = F_{18} + F_{17} = 4181
- F_{20} = F_{19} + F_{18} = 6765
Vastuse avalikustamine
Nüüd sina. Vali probleem, või kirjuta või joonista oma. Iga samm, pilt, vastus peidetud, kuni küsid.
Tasuta konto lisab märkmeid igale õppetunnile, ülestähenduse, oma lahendatud probleemide kohta ühes kohas ja juhendaja kohta, kellelt võid küsida selle lehekülje kohta. Matemaatika ise on avatud kõigile, allkirjastatud või mitte.
Registreeru SisselogimineSiin kasutatavad sümbolid
Koputage kõiki sümboleid, mis on mõeldud täieliku definitsiooni, pildi ja iga tähe all.
Kuidas: Sequences
- Each Fibonacci number is the sum of the two before it.
Küsimusi, mida inimesed küsivad
Why are primes so important?
Every integer factors into primes in exactly one way, so primes are the atoms of multiplication. Cryptography relies on that factoring being easy to state and hard to do.
How do I tell whether a big number is prime?
Trial division up to the square root works for small numbers. For large ones, probabilistic tests (Miller-Rabin) give an answer that is wrong with negligible probability, and deterministic tests (AKS) exist but are slower.
Rohkem Number Theory
Prime factorisationPrime numbersGCD and LCMModular arithmeticDivisorsNumber basesDiophantine equationsFermat's little theorem and Euler's theoremRSA: cryptography from number theory