- #1
jaychay
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Please help me
Thank you in advance
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SUMMARY
The discussion focuses on evaluating the limit of a mathematical expression involving factorials and polynomial terms as \( k \) approaches infinity. The specific limit to evaluate is \( \lim_{k \to \infty} \left| \frac{[3(k+1)]!}{(k+1)(k+2)} \cdot \frac{k(k+1)}{(3k)!} \right| \). Participants emphasize that the series is positive, suggesting that absolute values in the limit expression are unnecessary. The conclusion drawn is that understanding the behavior of factorial growth relative to polynomial terms is crucial for evaluating such limits.
PREREQUISITES- Understanding of limits in calculus
- Familiarity with factorial notation and properties
- Knowledge of series convergence and divergence
- Basic algebraic manipulation skills
- Study the properties of factorial growth compared to polynomial growth
- Learn about the Ratio Test for series convergence
- Explore advanced limit evaluation techniques in calculus
- Investigate the use of Stirling's approximation for factorials
Students in advanced mathematics, particularly those studying calculus and series, as well as educators looking for examples of limit evaluation techniques.
Please help me
Thank you in advance
- #2
jaychay
- 58
- 0
This is my work
I am struggle at this point
- #3
skeeter
- 1,103
- 1
\[ \lim_{k \to \infty} \left| \frac{[3(k+1)]!}{(k+1)(k+2)} \cdot \frac{k(k+1)}{(3k)!} \right| \]
\[ \lim_{k \to \infty} \left| \frac{k(3k+3)(3k+2)(3k+1)}{(k+2)}\right| \]
evaluate the limit ... what can you conclude?
\[ \lim_{k \to \infty} \left| \frac{k(3k+3)(3k+2)(3k+1)}{(k+2)}\right| \]
evaluate the limit ... what can you conclude?
- #4
Prove It
Gold Member
MHB
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Also, keep in mind it's a positive termed series, so the absolute values (while not incorrect) are unnecessary.
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