python Estimate p p can be computed using the following seri

python

Estimate p) p can be computed using the following series:

m(i)=4(1-1/3+1/5-1/7 +.....+((-1)^(i+1))/(2i-1))

Write a function that returns m(i) for a given i and write a test program that dis- plays the following table:

i

m(i)

Solution

Please find the required program along with its output. Please see the comments against each line to understand the step.

import math # This will import math module

def m(i):   # function that return value of m(i) for input i
   sum = 0  
   for j in range(1,i+1):   #iterate loop till i+1 times
       sum = sum + (math.pow(-1,j+1)/((2*j)-1))   #summation of the given series
   sum = 4 * sum  
   return float(sum)   #return number
  
  
print (\"i\\t m(i)\")   #print the output
print (\"1\\t\", round(m(1),4))
print (\"101\\t\", round(m(101),4))
print (\"201\\t\", round(m(201),4))
print (\"301\\t\", round(m(301),4))
print (\"401\\t\", round(m(401),4))
print (\"501\\t\", round(m(501),4))
print (\"601\\t\", round(m(601),4))
print (\"701\\t\", round(m(701),4))
print (\"801\\t\", round(m(801),4))
print (\"901\\t\", round(m(901),4))
      

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OUTPUT :