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I have a sequence $$ \frac{44}{24} , \frac{50}{24}, \frac{54}{24}, \frac{57}{24}, ...$$ Since this is not arithmetic nor geometric series could someone help me find the nth term, please?

I know that the difference between the terms is in harmonic progression i.e. $$ \frac{1}{4}, \frac{1}{6}, \frac{1}{8}...$$ But, I don't know how would this help.
Thanks a lot!
By the way, I'm really new here, so I'd really love some suggestions if I did something wrong or anything like that!

User4339
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  • Unless I am missing something, I would call $ \frac{44}{24} , \frac{50}{24}, \frac{54}{24}, \frac{57}{24}, ...$ a sequence rather than a series. Welcome to Math Stack. – 311411 Feb 12 '22 at 14:42
  • Oh, yeah sry! Thank you! I hope this would be a nice experience! – User4339 Feb 12 '22 at 14:43
  • Not sure what you are hoping for. As you are surely aware, there is no simple closed formula for $\sum \frac 1n$. – lulu Feb 12 '22 at 14:46
  • @lulu since there is no closed formula for this, I cannot find the nth term for this sequence? – User4339 Feb 12 '22 at 14:50
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    What does "cannot find" mean? Of course you can find it, in terms of $\sum \frac 1n$. My point is just that there isn't some simple closed formula for it, much as one might like one. – lulu Feb 12 '22 at 14:54
  • @lulu So by using ∑1/n I can get the nth term, but how? – User4339 Feb 12 '22 at 14:58
  • See this question and others that come up by searching sum of harmonic series I would call this a duplicate. – Ross Millikan Feb 12 '22 at 14:58
  • Well, just copying what you wrote, it is $a_n=\frac {44}{24}+\frac 12\times \sum_{k=2}^n \frac 1k$. – lulu Feb 12 '22 at 14:59
  • @lulu and Ross Thank you both of you! I got it! – User4339 Feb 12 '22 at 15:01

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