Let's say we start with the number one, then we add $(1/1)$. Now we have $2$. Then we do $2 + (1/2)$. Now we have $2.5$. Then we do $2.5$ plus $(1/2.5)$. If we continue this forever, I am fairly sure this diverges. However, I am wondering whether there is an implicit formula for the $n$th term of this sequence. For example: $A(1)=1$, $A(2)=2$, $A(3)=2.5$, and so on.
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Each time you are adding a number greater than or equal to $\frac{1}{n}$. That should be a clue to show that this is divergent. – Neil A. Mar 22 '19 at 02:39
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Thanks Neil, this is interesting. Any thoughts about an implicit function? – Rdog60 Mar 22 '19 at 02:47
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This has come up a number of times: here,here,here – Ross Millikan Mar 22 '19 at 03:03