Contents

COMPARING TWO SERIES FOR VALUE OF PI

Language : Matlab 2007a Authors : Autar Kaw Last Revised : October 30, 2008 Abstract: This program compares results for the value of pi using a) Gregory series and b) Ramanajun series

clc
clear all
clf
format long
disp('This program compares results for the value of')
disp('pi using a) Gregory series and b) Ramanajun series')
disp('  ')
disp('Gregory series')
disp('pi=sum over k from 0 to inf of (4*((-1)^k/(2*k+1))')
disp('  ')
disp('Ramanajun Series')
disp('1/pi=sum over k from 0 to infinity of 2*sqrt(2)/9801*((4k)!*(1103+26390k)/(k!)^4*396^(4*k))')

This program compares results for the value of
pi using a) Gregory series and b) Ramanajun series
  
Gregory series
pi=sum over k from 0 to inf of (4*((-1)^k/(2*k+1))
  
Ramanajun Series
1/pi=sum over k from 0 to infinity of 2*sqrt(2)/9801*((4k)!*(1103+26390k)/(k!)^4*396^(4*k))

INPUTS.

%If you want to experiment this the only parameter
% you should and can change.
% Maximum number of terms
n=30;

PROGRAM

GREGORY SERIES

pi_gregory=0;
for i=1:1:n
    pi_gregory=pi_gregory+(-1)^(i+1)*4*(1/(2*i-1));
    pi_gregory_array(i)=pi_gregory;
end

RAMANUJAN SERIES

pi_ram=0;
for i=0:1:n-1
    pi_ram=pi_ram+2*sqrt(2)/9801.0*(factorial(4*i))*(1103.0+26390.0*i)/((factorial(i)^4)*(396)^(4*i));
    pi_ram_array(i+1)=1/pi_ram;
end

THE OUTPUT

disp(' ')
fprintf('\nNumber of Terms = %g',n)
fprintf('\nGregory Series Value = %g',pi_gregory)
fprintf('\nRamanujan Series Value = %g',1/pi_ram)
disp( '   ')

 

Number of Terms = 30
Gregory Series Value = 3.10827
Ramanujan Series Value = 3.14159   

PLOTTING THE TWO SERIES AS A FUNCTION OF TERMS

x=1:1:n;
hold on
xlabel('Number of terms')
ylabel('Value of pi')
title('Comparing Gregory and Ramanujan series')
plot(x,pi_gregory_array,'color','blue','LineWidth',2)
hold on
plot(x,pi_ram_array,'color','black','LineWidth',2)
legend('Gregory Series','Ramanajun Series',1)

Published with MATLAB® 7.3