Loop

I have three files: f1, f2, and f3. If each file has a number of lines such that
f1

The sky is blue
The earth is round
This is paper

f2

aaaaaaaaaa
bbbbbbbbbbbbb
cccccccccc

f3

kkkkkkkkkkkkkkkkkkk
lllllllllllllllllllllllllll
ooooooooooooooo

Now I want to write a program that goes to file one, grabs the first line, then goes too file 2, grabs the first line, and finally goes to file 3 and grabs the first line.
It then returns to file1, grabs the second line, then goes to f2, grabs the 2nd line, and goes to f3, grabs the 2nd line.
Finally, it foes to file 1, grabs the 3rd line and so on until it all three files are read and one single file is created.
I tried the following script and it is not doing what I want. That's where I would need some help.

for i in line
do
   while read line
   do
      echo $line >> lline
   done<f1
   while read line
   do
      echo $line >> lline
   done<f2
   while read line
   do
      echo $line >> lline
   done<f3
done

The desired output is:

The sky is blue
aaaaaaaaaa
kkkkkkkkkkkkkkkkkkk
The earth is round
bbbbbbbbbbbbb
lllllllllllllllllllllllllll
this is paper
cccccccccc
ooooooooooooooo

How can I fix my code?

Why write a script when this can be done via a command:

paste -d "\n" /tmp/f1 /tmp/f2 /tmp/f3

And here is the output from above:

The sky is blue
aaaaaaaaa
kkkkkkkkkkkkkkkkkkk
The earth is round
bbbbbbbbbbbbb
lllllllllllllllllllllllllll
This is paper
cccccccccc
ooooooooooooooo

Excellent Dude2cool! It works fine, exactly what I am looking for.