"So it would have served no purpose."
Translation:Alors cela n'aurait servi à rien.
It came back with the correct answer as Alors ça n'aurait pas servi .....That would be translated as ....So it would not have served....Which is not what the English phrase says. My answer....Alor ça n'aurait rien servi....was rejected. I wonder why?
My long answer has vanished!
"servir à rien" is a phrase that means "be of no use"
To quote from another post:
the verb servir can be both transitive and intransitive. As a transitive verb it can mean 'to serve' and as an intransitive verb it can mean 'to be useful'.
If you use servir as an intransitive verb then
servir à quelque chose - to be useful for something.
servir de quelque chose - to be used as something.
I also do not think that you sentence is grammatically correct French. After looking for examples I found it was continuously changed to the answer above. To see what I mean go to https://www.linguee.com/french-English
and type in n'aurait rien servi to see what I mean.