The latest software is 7.1.1.
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7.1.1 is a maintenance fix not a major upgrade any one whom has 7.0 or 7.1 should apply the update. Regarding this issue with iPad crashing frankly go to an apple store and request apple replace the iPad. I have delivered close to 100 iPad Air iPads non of which have suffered any issues of this nature. Further to this I suggest connect the iPad to a computer and do a factory restore do not sync the back up. Test the iPad with stock apps only and see what happens. At the end of the day either you have app or apps causing the crashes or faulty hardware. Hope that helps.