If you want to edit the file in place, most shell tools won't help you because when you open a file for writing, you only have a choice of truncating it (>) or appending to it (>>), not overwriting existing contents. dd is a notable exception. See Is there a way to modify a file in-place?Is there a way to modify a file in-place?
export LC_ALL=C
lines_to_keep=$((linenum1 - 1))
lines_to_skip=$((linenum2 - linenum1 + 1))
deleted_bytes=$({ { head -n "$lines_to_keep"
                    head -n "$lines_to_skip" >&3;
                    cat
                  } <big_file | dd of=big_file conv=notrunc;
                } 3>&1 | wc -c)
dd if=/dev/null of=big_file bs=1 seek="$(($(wc -c <big_file) - $deleted_bytes))"
(Warning: untested!)
 
                 
                 
                