What is the Fibonacci Sequense?
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is:http://en.wikipedia.org/wiki/Fibonacci_number\nclick to see.
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Having researched this topic as far as possible online, I found very few helpful resources.\n\nWhile the result you mention, using the subsequence 6(5)^n, is intriguing, I suspect that other sequences will yield vastly different bounds on the index.  In particular, is it not true that any prime number p always has a corresponding Fibonacci number F(p+1) of which it is a factor?\n\nGood luck with your own research!
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21, 34  Yes it's called the Fibonacci series.  Each number is the sum of the previous two.\n\nWhat I don't understand is as a result of asking a valid question to expand your knowledge, so many people gave you such rude replys.\n\nI hope this helps, have a good day.
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adding the number next in sequence. first added 1, then 2, then 3.....
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for (i=1,t=1,cosx=1;i<=n;++i)\n{\n  t=(-1)*(t*x*x)/((2*i)*(2*i-1);\n  cosx += t;\n}
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here we are talking about a  sequence , so we try to get the formula of the sequence than the result.\nBut the proposed solution that 1=5 it's completly  wrong
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Starting with 0, the sequence is the square of that number:\n\nf(n) = n^2. \n\nf(0) = 0 (0^2)\nf(1) = 1 (1^2)\nf(2) = 4 (2^2)\nf(3) = 9 (3^2)\nf(4) = 16 (4^2)\nf(5) = 25 (5^2)\netc.\n\nNote, it isn't clear if your indexes are going 0,1,2,3,4,... or are going in descending order 0,-1,-2,-3,-4... the resulting sequence would be the same.\n\nf(0) = 0 (0^2)\nf(-1) = 1 (-1^2)\nf(-2) = 4 (-2^2)\nf(-3) = 9 (-3^2)\nf(-4) = 16 (-4^2)\nf(-5) = 25 (-5^2)\netc.
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Binet's formula is correct but inconvenient, and z_o_r_r_o is simply wrong.\n\nIt is fastest to calculate in pairs, instead of singly.\n\nnot only is (F16, F17) is easily obtained from (F15, F16) by the definition of Fibonacci numbers\n\nbut, brilliantly,\n\n(F15, F16) is easily obtained from (F7, F8)\n\nbecause for example F16 = F8 * (F8 + 2 * F7) = 21 * (21 + 26) = 987, and F15 = F8 * F8 + F7 * F7 = 21^2 + 13^2 = 610.\n\nSo whatever number you want, by progressively halving the index when it is even or subtracting 1 when it is odd, you can get down to an easily looked-up Fibonacci number in LOGARITHMIC time.
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Leonardo Pisano Fibonacci 1170 – 1250 \nFibonacci series, Introduced decimal system ( Liber abaci which means "The Book of Calculations" . There area few more but even that is impressive http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html  http://www-history.mcs.st-and.ac.uk/Mathematicians/Fibonacci.html \nVery little was documented during the period encompassing 6-12 centuries in Europe http://en.wikipedia.org/wiki/History_of_science_in_the_Middle_Ages
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These three sequntal clock wise numbers \n2+3+4 --> 9+4 --> 1 (adding the last no.(4)\nBut not works for all
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Fibonacci Numbers are the sequence of numbers defined recursively by:\n\nF(0)= 0\n\nF(1)= 1\n\nF(n)= F(n-2)+F(n-1)   for n > 1.\n\ni.e., \n0,1,1,2,3,5,8,13,21,34,55.......\n\nThe earliest known reference to Fibonacci numbers is contained in a book on meters by an Indian mathematician named Pingala called Chhandah-shastra (500 BC). In the West, it was first studied by Leonardo of Pisa, who was also known as Fibonacci (c. 1200)
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ok, this is found in the 4th quadrant, the order is as follows\n\n(x,y) 1st\n(-x,y) 2nd\n(-x,-y) 3rd\n(x,-y) 4th\n\nhope this helps\n\nmatttlocke
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Nine (9) - before 10 and after 11\nOne (1) - before 2 and after 0\nOne (1) - before 2 and after 0
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Consecutive numbers differ by 1.\nIf the first one is n, then the second one is n+1\nThat means the third one is the second number plus one (n+1)+1 = n+2\nThe fourth one is (n+2)+1 = n+3\nand the fifth one is (n+3)+1 = n+4\nAdd them altogether\nn + n+1 + n+2 + n+3 + n+4 = 5n + 10
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Arithmetic sequence:  1, 2, 3, 4, 5, 6, 7\nGeometric sequence:  1, 2, 4, 8, 16, 32, 64
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the correct sequence is:-\n\nthousand,million,billion,Trillion, Quadrillion, Quintillion, Sextillion, Sept, Oct, non, deci .....\ni dont know more than that.
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The Fibonacci numbers form a sequence defined recursively by:\n\nF(n)= 0 if n = 0;\n      1 if n = 1;\n      F(n-1)+F(n-2) if n > 1.\n\nIn other words: one starts with 0 and 1, and then produces the next Fibonacci number by adding the two previous Fibonacci numbers. The first Fibonacci numbers for n = 0, 1, … are\n\n0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, …\n\nThe earliest known reference to Fibonacci numbers is contained in a book on meters by an Indian mathematician named Pingala called Chhandah-shastra (500 BC). As documented by Donald Knuth in The Art of Computer Programming, this sequence was described by the Indian mathematicians Gopala and Hemachandra in 1150, who were investigating the possible ways of exactly bin packing items of length 1 and 2.\n\nAs was pointed out by Johannes Kepler, the ratio of consecutive Fibonacci numbers, that is:\n\nF(n+1)/F(n),\n\nconverges to the golden ratio φ (phi).