## 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;
```

## 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)
```