Not discussed (that I can see), the real problem is the loop variable -- because the loop ends with ' <= n', which means if n is the largest unsigned integer, this is an infinite loop. One easy thing UB is useful for is proving these types of loop terminate (as overflowing would be UB).
gcc doesn't seem to implement this optimization at all.
Technically it should be possible for the <=n case, too: An infinite loop is undefined behavior, so the compiler is allowed to assume it doesn't happen. But I guess (for good reasons) compiler writers are reluctant to exploit that too heavily (or it's just about ordering of optimization passes).
EDIT: I had a quick look to see why the obvious equation ( n (n+1))/2 ) didn't just work. The only problem for large n is you need to do the 'n (n+1)' in a bigger type (it doesn't technically matter if the n*(n+1) overflows, you just need a bigger type), so when you divide by 2 you get the right value in the top-most byte of 'unsigned int'.