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Bachelier
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sum n/(n^2 + 2 sqrt(n) + 9), n=0 to infinity
How do I prove it diverges?
How do I prove it diverges?
Does the sum of this rational function diverge with the Limit Comparison Test?
- Thread starter Bachelier
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SUMMARY
The sum of the rational function ∑ n/(n² + 2√n + 9) from n=0 to infinity diverges when analyzed using the Limit Comparison Test (LCT) with the harmonic series. The LCT is an effective method for determining the convergence or divergence of series involving rational functions. In this case, the comparison with the harmonic series, which is known to diverge, confirms the divergence of the given series.
PREREQUISITES- Understanding of the Limit Comparison Test (LCT)
- Familiarity with the harmonic series
- Knowledge of rational functions
- Basic concepts of series convergence and divergence
- Study the Limit Comparison Test in detail
- Explore the properties and behavior of the harmonic series
- Learn about other convergence tests such as the Ratio Test and Root Test
- Investigate rational functions and their limits
Mathematics students, educators, and anyone studying series convergence, particularly those focusing on calculus and analysis.
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