How do I extract the first N lines from a big text file to a separate file via Bash?

Method 1

sed 100q $file > output.txt

stackoverflow.com/a/1411145

Method 2

head -n 100 $file > output.txt

stackoverflow.com/a/1411078

Method 3

sed -n '1,100p;101q' $file > output.txt

How do I extract a range of lines from a big text file to a separate file via Bash?