We know that $\sum_{i=1}^{ \infty} \frac{1}{i^{2}}= \frac{ \ \ \pi^ {2}}{6}$. On the other hand $\sum_{i=1}^{n} \frac{1}{i^{2}}$ also is convergent but Does not have a routine answer based on the function. Is there an example of series such that Both the infinite state and the finite state of that answer are routine?
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2The answer is often just left as-is or shorthanded as $H_{n,2}$ as found here. You won't be getting any answer better than that, it doesn't have a clean closed form otherwise. – JMoravitz Oct 20 '22 at 16:55
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Is there an example of this type of series such that Both the infinite state and the finite state of that answer are routine? – ebrahimi Oct 20 '22 at 17:06
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Per the top answer in the linked question... no. – JMoravitz Oct 20 '22 at 17:07
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Thank you for answer – ebrahimi Oct 20 '22 at 17:18