Calculating pi using bash
I see a few things that could allow you to improve your program.  First, though, I don't consider myself a bash expert, so there may well be better ways of doing these things.

Use a "shebang" line

As this question points out, you should always use a "shebang" line for your bash scripts.  So the first line would be:

#!/usr/bin/env bash


Pass values as arguments

Rather than prompting for the SCALE value, it's generally better to use a command line argument.  That way, the script can be reused by other shell scripts.

Provide a stopping mechanism

As each term is calculated, eventually, it will be equal to zero given the passed scale.  This suggests a mechanism for stopping: check each term for 0 before adding it.

Indent do and while loops

I don't know of a bash style guide (there probably is one!) but I like to see the contents of loops indented to make it easier to read.

Putting it all together

Here's a modification of your script with all of these suggestions implemented:

bashpi.sh

#!/usr/bin/env bash
SCALE=$1
VALUE=2
PI=0
FITNESS=1
DELTA=3
while [ $(echo "$DELTA==0" |bc) != "1" ]
do
    PI=$(echo "$PI+$DELTA" | bc)
    DELTA=$(echo "scale=$SCALE;(4/($VALUE*($VALUE+1)*($VALUE+2)))-(4/(($VALUE+2)*($VALUE+3)*($VALUE+4)))" | bc)
    VALUE=$(($VALUE+4))
    FITNESS=$(($FITNESS+1))
    echo "###############"
    echo "--&gt; $FITNESS // $VALUE"
    echo "$PI"
done


To better understand how this works, you can replace the three echo statements with this one:

echo "DELTA = ${DELTA} --&gt; ${FITNESS} // ${VALUE} : ${PI}"


Sample output

With ./bashpi.sh 4, and the modified echo above I get this output:

DELTA = .1333 --&gt; 2 // 6 : 3
DELTA = .0064 --&gt; 3 // 10 : 3.1333
DELTA = .0012 --&gt; 4 // 14 : 3.1397
DELTA = .0003 --&gt; 5 // 18 : 3.1409
DELTA = .0001 --&gt; 6 // 22 : 3.1412
DELTA = .0001 --&gt; 7 // 26 : 3.1413
DELTA = .0001 --&gt; 8 // 30 : 3.1414
DELTA = 0 --&gt; 9 // 34 : 3.1415