Why won't my 2GB micro SD card work?

I just bought a 2GB micro SD card with a normal SD adapter to transfer stuff from my phone to my computer and vice versa, but when I put the micro card in my phone it doesn’t recognise it and when I put it in the adaptor and put it in the computer it doesn’t recognise it there either. I think my phone, an LG TU500 doesn’t recognise anything bigger than 1GB or so I’ve just been told, but shouldn’t my computer still recognise it? I’ve used my camera’s normal 2GB SD card in the computer just fine.