according to crucial , you can upgrade it to 4GB on both aspire 4720 and 4920 , i think you want info for 4720, so here it is...
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Memory Type: DDR2 PC2-6400, DDR2 PC2-5300, DDR2 (non-ECC)
Maximum Memory: 4GB
Slots: 2
How much memory your Windows OS will recognize depends on which version of Windows you are running. 32-bit versions of Windows will see (and utilize) only 3GB or 3.5GB. To utilize more memory, install a 64-bit version of your OS.
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http://edge.crucial.com/store/mpartspecs.aspx?mtbpoid=62752D93A5CA7304
crucial is great website to see if your RAM can be upgraded.... there memory is kind of expensive, so you can also get it from ebay