vergebens
in vain
Describes an action or attempt that remains unsuccessful and does not achieve the desired goal.
Wir haben stundenlang nach dem verlorenen Schlüssel gesucht, aber vergebens.
We searched for the lost key for hours, but in vain.

in vain
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in vain
Describes an action or attempt that remains unsuccessful and does not achieve the desired goal.
Wir haben stundenlang nach dem verlorenen Schlüssel gesucht, aber vergebens.
We searched for the lost key for hours, but in vain.

The word 'vergebens' (in vain) is related to the verb 'vergeben' (to forgive/to give away). The original idea is that effort or expense was 'given away for nothing' and therefore brought no success.
All seine Bemühungen, sie zu überzeugen, waren vergebens.
All his efforts to convince her were in vain.
'Vergebens' (in vain) often stands at the beginning or end of a sentence to emphasize the lack of success. It can also stand directly after the conjugated verb.
Vergebens versuchte er, die Tür zu öffnen.
In vain, he tried to open the door.
'Vergebens' (in vain) is often combined with verbs of trying, waiting, or searching. Typical phrases are 'vergebens warten' (to wait in vain), 'vergebens suchen' (to search in vain), and 'sich vergebens bemühen' (to try in vain).
Ich habe vergebens auf eine Antwort von ihm gewartet.
I waited in vain for a reply from him.
The word 'vergebens' (in vain) belongs more to written language or an elevated style. It often sounds somewhat more formal or literary.
Die Hoffnung auf eine schnelle Lösung erwies sich als vergebens.
The hope for a quick solution proved to be in vain.
successful
'erfolgreich' and 'vergebens' are clear opposites. 'erfolgreich' means that a desired goal has been achieved. 'vergebens', on the other hand, describes an attempt or action that did not achieve anything. The grammar is also important: 'erfolgreich' is an adjective and can describe people, actions, or results. 'vergebens' is an adverb and usually describes how someone tries to do something.

Du rufst vergebens an, weil das Büro heute geschlossen ist.
You are calling in vain because the office is closed today.
Nach mehreren Gesprächen war die Suche nach einer neuen Wohnung erfolgreich.
After several conversations, the search for a new apartment was successful.