How to sum reciprocals in bash?

Question

I am attempting to find the sum of a list of numbers' reciprocals. To illustrate what I am trying to do, here's a basic example:

With the file:

1  
2  
3  
4

I would be trying to find the sum of 1/1, 1/2, 1/3 and 1/4. Is there a simple bash one-liner to do this? (I am new to bash, so explanations would be welcome!)

Answer 1

You could do something like this:

sed 's|^|1/|' file | paste -sd+ | bc -l

• sed 's|^|1/|' prepends 1/ to every line
• paste -sd+ joins all lines with a plus sign creating an arithmetic expression 1/1+1/2+1/3+1/4
• bc -l evaluates that arithmetic expression and outputs the result

Answer 2

If you're looking for an arithmetical progression, you can use this bash one-liner using the bc command

d=0; for c in {1..4}; do d=`echo "$d + 1/$c" | bc -l`; done; echo "$d"

Its output is 1 + 0.5 + 0.3333 + 0.25 =

2.08333333333333333333

It works by

1. Setting a variable named d to 0
2. Creating a for loop that counts from 1 to 4
3. In the for loop it sets the d variable to the new value $d + 1/$c passed to the bc -l command executing the arithmetic
4. And outputs the value with an echo command