How can I update iPad 1 from iOS 5.1.1 to iOS 7.1?
I tried checking for updates but I get a message "your software is up to date".
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The last version of iOS capable of being installed on an iPad 1 is iOS 5.1.1 and since this is the version that you are currently on there are no updates available.
This just isn’t possible.
From Apple's Support:
iOS 6 is not available for the iPhone 3G or earlier, iPod touch (3rd generation) or earlier, and iPad (1st generation).
iPhone 4 and later
iPad 2 and later
iPod touch (5th generation)
System requirements iPhone 4s or later iPad 2 or later iPad mini or later iPod touch (5th gen)
According to this site, the latest version of iOS supported by the original iPad is 5.1.1, so the answer is that within the constraints of the question (no jailbreaking, etc.) you can't upgrade beyond 5.1.1. Sorry.