I've written a little program to calculate pi using the Nilakantha series

For this formula, take three and start alternating between adding and subtracting fractions with numerators of 4 and denominators that are the product of three consecutive integers which increase with every new iteration. Each subsequent fraction begins its set of integers with the highest one used in the previous fraction. Carry this out even a few times and the results get fairly close to pi.  (http://www.wikihow.com/Calculate-Pi)

I don't really understand other ways of calculating pi, or they take too long to perform.

So this is the code I came up with

echo "Enter scale please"
read SCALE
VALUE=2
PI=3
FITNESS=1
while true
do
PI=$(echo "scale=$SCALE;$PI+(4/($VALUE*($VALUE+1)*($VALUE+2)))-(4/(($VALUE+2)*($VALUE+3)*($VALUE+4)))" | bc)
VALUE=$(($VALUE+4))
FITNESS=$(($FITNESS+1))
echo "###############"
echo "--> $FITNESS // $VALUE"
echo "$PI"
done

I would really like to know how to detect when I get the same output multiple times, so I can tell the program to terminate when it has reached the most accurate version of pi possible.

Also if you have other suggestions on how to improve the code and/or know a better way of calculating pi (with some explaination), I would like to hear.

I've written a little program to calculate pi using the Nilakantha series:

For this formula, take three and start alternating between adding and subtracting fractions with numerators of 4 and denominators that are the product of three consecutive integers which increase with every new iteration. Each subsequent fraction begins its set of integers with the highest one used in the previous fraction. Carry this out even a few times and the results get fairly close to pi.  (http://www.wikihow.com/Calculate-Pi)

I don't really understand other ways of calculating pi, or they take too long to perform.

echo "Enter scale please"
read SCALE
VALUE=2
PI=3
FITNESS=1
while true
do
PI=$(echo "scale=$SCALE;$PI+(4/($VALUE*($VALUE+1)*($VALUE+2)))-(4/(($VALUE+2)*($VALUE+3)*($VALUE+4)))" | bc)
VALUE=$(($VALUE+4))
FITNESS=$(($FITNESS+1))
echo "###############"
echo "--> $FITNESS // $VALUE"
echo "$PI"
done

I would really like to know how to detect when I get the same output multiple times, so I can tell the program to terminate when it has reached the most accurate version of pi possible.

Also if you have other suggestions on how to improve the code and/or know a better way of calculating pi (with some explanation), I would like to hear.