Are NDS games the same to be downloaded for NDSi?

I bought my son a Nintendo DSi and also bought an R4i, i want to know if i still download the same games that i used to download for a nintendo DS.

Yes, the DSi and the R4i will play the same ROMs that the DS can.But a warning, do not upgrade your DSi to 1.4 firmware or else it may block your R4i from working. There are so many R4i's that it is hard to tell if it is 1.4 compatible or not (some are, some aren't).