I am working on a program that calculates the Reciprocal Fibonacci Constant (the infinite summation of the Fibonacci numbers.) It calculates every term upto it's error:

I have an program but it only goes to 1474 terms and I need to get to about 10000 terms. It returns an error:

``Traceback (most recent call last):File "/Users/jaddvirji/Desktop/PapaTechChallenges/Challenge2/Part1/main.py", line 23, in <module>curf.write(str(Decimal(fibConstant(x))))File "/Users/jaddvirji/Desktop/PapaTechChallenges/Challenge2/Part1/main.py", line 18, in fibConstantreturn (1.0 / fib(n)) + fibConstant(n - 1.0)File "/Users/jaddvirji/Desktop/PapaTechChallenges/Challenge2/Part1/main.py", line 12, in fibreturn long(((phi**n) - (1-phi)**n) / 5**0.5)OverflowError: (34, 'Result too large')``

And my code is:

``#!/usr/bin/env pythonprint "(C) COPYRIGHT JADD VIRJI 2013. ALL RIGHTS RESERVED."from decimal import *import time as timport syssys.setrecursionlimit(10000)phi = (1+(5**0.5))/2def fib(n):return long(((phi**n) - (1-phi)**n) / 5**0.5)def fibConstant(n):if(n == 1):return (1.0 / fib(n))else:return (1.0 / fib(n)) + fibConstant(n - 1.0)x = 1while True:curf = open(str(x)+" term.txt","w")curf.write(str(Decimal(fibConstant(x))))curf.close()x = x+1print Decimal(x)print "DONE. THANKS FOR USING."``

Also, Every result from about 200 terms above is the same (and wrong.)

Does anybody know how to fix these problems?

EDIT: I have a feeling that the problems after ~200 terms are because of floating point errors with the Binet Fibonacci calculation. How do I make these decimals go on forever?

Try storing the values of `fibConstant` in a list. Then for each subsequent calculation, you only need to call the last value of the list instead of recalculating. For example:

``````from math import sqrt

phi = (1 + sqrt(5)) / 2.

def fib(n):
return (phi**n - (1-phi)**n) / sqrt(5)

fib_constant_list = [1./fib(1)]
def fib_constant(n):
new_fib_c = (1./fib(n) + fib_constant_list[-1])
fib_constant_list.append(new_fib_c)
return new_fib_c

n = 2
N_MAX = 1000
while n < N_MAX:
print fib_constant(n)
``````

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