Hello everyone,
I’m currently studying infinite series in my calculus course and have encountered some concepts that I find quite challenging, particularly the criteria for convergence. I’ve read about the Comparison Test, Ratio Test, and Root Test, but I’m struggling to apply these tests effectively in different scenarios.
To give you some context, I’ve worked through a few examples, but I often find myself unsure about which test to use or how to justify my choice. For instance, when faced with a series like ∑n=1∞n22n\sum_{n=1}^{\infty} \frac{n^2}{2^n}∑n=1∞2nn2, I initially thought the Ratio Test would be appropriate, but I’m not confident in my analysis.
Could someone provide guidance on the following:
How do you determine which convergence test to apply to a given series?
Are there any tips or tricks for recognizing when a series converges or diverges?
Can you provide examples of series where different tests yield different insights?
I believe this information will not only help me but also others who might be grappling with similar issues. Thank you for your assistance!
