More specifically, how would you evaluate the below formula? $$\lim_{n\to\infty}\sum_{k=n/2}^{n}\frac{1}{k}$$ I know that the harmonic series starting at any point diverges, but when we limit it in this way, does the series diverge or converge?
If it diverges:
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How might you determine that?
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Is there some $d$ that we can replace with $2$ to make the sequence converge?
If it converges:
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What does it converge to, and how might you determine that?
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The sequence must converge for any $d>2$. Is there a formula for the series generalized for any $d$?
from Hot Weekly Questions - Mathematics Stack Exchange
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