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The series does not converge, because as you observe, the partial sums $1,0,1,0,\ldots$ oscillate and do not approach a single limit. There are various ways to assign values to some divergent series,. @coffeemath Debatable: you can write Hn = S2 n + 1 n! Where S denotes Stirling numbers of the first kind. But it may not be considered a "closed form", since Stirling numbers are not much more easy. Jan 15, 2013 · Possible Duplicate: How do I convince someone that $1+1=2$ may not necessarily be true? I once read that some mathematicians provided a very length proof of $1+1=2$. Can you think.
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