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> Fibonacci series
-
F
1
= 1;
F
2
= 1;
F
n
=
F
n
-1
+
F
n
-2
Each member of the series is the sum of the previous two
-
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597,
2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418,
317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465,
14930352, 24157817, 39088169, 63245986, 102334155, 165580141, 267914296,
433494437, 701408733, 1134903170, 1836311903, 2971215073, 4807526976,
7778742049, 12586269025, 20365011074, 32951280099, 53316291173,
86267571272, ...
-
The ratio of consecutive terms,
F
n
+1
/
F
n
,
tends to the golden ratio, (1+
5)/2
= 1.61803...