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What is the first term in the Fibonacci sequence to contain 1000 digits?
Wiki User
∙ 11y ago
After the first few numbers in the Fib sequence, Fib(n) is very nearly equal to (phi)n / sqrt(5) where phi is the Golden Ratio = [1+sqrt(5)]/2
[The difference is around 0.00003 by Fib(20)]
So you want the smallest n such that (phi)n / sqrt(5) ≥ 10999
Taking logs,
n*log(phi) - 0.5*log(5) ≥ 999
n*log(phi) ≥ 999 + 0.5*log(5) = 999.349
n ≥ 999.349/log(phi) = 999.349/0.2090
So n = 4781
Wiki User
∙ 11y ago
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When did Leonardo Fibonacci discovered the Fibonacci numbers?
Leonardo Fibonacci first recorded his sequence in his book Liber Abaci, which was published in 1202.
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What are the first three numbers in the Fibonacci sequence?
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