slightly ashamed that i know what that means and even laughed
Now here's some **** I understand
Exit pursued by a bear
Prove that two consecutive numbers from Fibonacci Series are always relatively prime.
"I want to raise my hand and say one thing. Those who complain about my love for the game or commitment to the game are clueless. These are the only 2 areas where I give myself 100 out of 100."
- Sachin Tendulkar, as told in an interview published in Bengali newspaper Anandabazar Patrika after his 100th International century (translated by weldone)
by contradiction and induction.
let f(n), f(n+1) be the nth fibonacci number for some integer n. suppose n=1. well... that's sort of trivial, i won't bother.
suppose true for some n=k ie. f(k) and f(k+1) are coprime.
suppose f(k+1) and f(k+2) are not coprime ie. there exists some non-trivial divisor d of both.
but f(k) = f(k+2) - f(k+1) so f(k) is also divisible by d. but this means that f(k), f(k+1) are not coprime - contradiction, qed, done.
+ time's fickle card game ~ with you and i +
get ready for a broken ****in' arm
Another question related to fibonacci numbers (I was asked this in an interview): What does the ratio of consecutive fibonacci number, f(k+1)/f(k) converge to as we go to as k->∞?
The part that was relatively easy was to find that ratio assuming convergence. But I don't known how to show there will be convergence in the first place. That will probably require university level calculus which I don't much remember (for every epsilon ε there exists a delta δ etc...)
EDIT: For limit of a sequence, you don't have δ but N.
Last edited by ankitj; 05-03-2013 at 07:20 AM.
Last edited by weldone; 05-03-2013 at 09:20 AM.
Probability of observing an accident in one hour period on an accident prone bridge is 10%. What is the probability of observing an accident in two hour period?
Don't mind if the candidate answers it after some hints. Is that too lenient?
yeah that's just 1 - 0.9^2 innit?
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