If the shell is
ksh (version 2020.0.0 and perhaps in others), what you need is this:
./file_1.txt >> file_2.txt 2>&1
That will redirect stderr to stdout which is being appended to file_2.txt. The
& lets the shell know that you are working with file descriptors instead of file names. The command that you have doesn't work because the syntax isn't valid for anything and hence the redirection can't be parsed by the shell.
The command above takes care of this by redirecting both the
file_2.txt as I explained.
bash, you can also use, provided by steeldriver:
./file_1.txt &>> file_2.txt
That does the same thing.
& means both stdout and stderr and
>> appends them both the
file_2.txt. I gave the first command initially because that's what I normally use due to it being what I learned first many years ago.
Neither works with
tcsh version 6.21.00 after testing. They both give, respectively,
Invalid null command. and
Ambiguous output redirect.