Nintendo 3DS Game Compatibility with Nintendo DSi: Not Possible

No. 3DS games do not work on any DS/DSi model.

• Hardware: 3DS has vastly more powerful CPU/GPU and stereoscopic screens.
• Cartridge: 3DS game cards are physically incompatible with DS slots.
• Software: 3DS OS and game code cannot run on DS hardware.

You need a 3DS/2DS/3DS XL to play 3DS games.