Solve Series Convergence: $\sum^{n=0}_{\infty}\frac{2n-1}{\sqrt{n^{5}+1}}

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The series $\sum^{n=0}^{\infty}\frac{2n-1}{\sqrt{n^{5}+1}}$ has been solved, confirming its convergence. The user initially sought assistance but realized the solution while typing their query. The discussion highlights the importance of engaging with the problem to facilitate understanding. Ultimately, the series converges, providing a resolution to the inquiry. This illustrates the value of persistence in solving mathematical problems.
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[SOLVED] Series convergence

Homework Statement




\sum^{n=0}_{\infty}\frac{2n-1}{\sqrt{n^{5}+1}}

Homework Equations





The Attempt at a Solution

 
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sorry - i fugured it out while i was typing it.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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