[Tutor] getting error while solving a series that estimates the value of pi

[Andre Engels]

On Mon, Jul 18, 2011 at 6:10 PM, surya k <suryak at live.com> wrote:

> Hi,
>
> The problem is to estimate the value of pi using the following series.
>  *1 / pi  = (( 2 * sqrt(2) )/ 9801 )  * SIGMA of k[ (4k)! (1103 + 26390*k)
> / (k!^ 4 ) * 396^(4k)  ]*
> *where k is [0, infinity)*
> * Problem is located at : ThinkPython Book, www.thinkpython.org
>    *Pg 89, Exercise 7.5, Think Python Book. *
> *
> *
> the series should be considered till the last term of the sigma must be <
> 1e-15
> I have written the below code :
>
> *# program estimates the value of pi*
> *# Ramanujan's series... *
> *import math*
> *
> *
> *def fact(n) : # def of factorial function.*
> *    if n > 0 :    *
> *       return n * fact(n-1)*
> *    if n == 0 :*
> *       return 1*
> *
> *
> *k = 0*
> *tot = 0*
> *temp1 = 0*
> *while k >= 0 and temp1 == 0 :*
> *
> *
> *      a = ( 2 * math.sqrt(2) ) / 9801 # first term before sigma *
> *      nu = fact (4*k) * (1103 + (26390*k) )  # numerator of series*
> *      de = pow( fact(k), 4 ) * pow ( 396, 4*k )  # denominator of series*
> *      *
> *      if de / nu > 1e-15 : *
> *            temp = nu / de*
> *            tot = tot + temp*
> *            temp1 = 0 *
> *            k = k + 1 *
> *      elif de / nu  == 1e-15 :*
> *             series = a * tot  *
> *             k = k + 1*
> *             temp1 = 0*
> *      elif de / nu < 1e-15 :*
> *             print series*
> *             temp1 = 1*
>
>
> I am getting the following error : which is completely surprising!
>
> *Traceback (most recent call last):*
> *  File "pi.py", line 30, in <module>*
> *    print series*
> *NameError: name 'series' is not defined*
>
> *
> *
> Thus I have removed name 'series' and replaced with  *a*tot, *
> now I am getting this error
>
> *Traceback (most recent call last):*
> *  File "pi.py", line 30, in <module>*
> *    print 1 / (a * tot)*
> *ZeroDivisionError: float divisio*n
>
>
>
> Thus I changed the first highlighted lines to
>
>  *nu = float (fact (4*k) * (1103 + (26390*k) ) )*
> *      de = float (pow( fact(k), 4 ) * pow ( 396, 4*k )) *
>
>
> now I am getting
>
> * Traceback (most recent call last):*
> *  File "pi.py", line 18, in <module>*
> *    de = float (pow( fact(k), 4 ) * pow ( 396, 4*k ) )*
> *OverflowError: long int too large to convert to float*
>
> *help me out of this problem, how could I fix this*
>
>
You have the definitions of numerator and denominator switched.

-- 
André Engels, andreengels at gmail.com
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