Math Problem Statement
find the above question's interval of convergence by some other test
Solution
It looks like you're referring to a previous question about finding the interval of convergence of a series. However, I don't have access to that question yet. Could you please provide the series or the specific details of the problem? Then, I can apply a different convergence test to determine the interval.
Alternatively, you can upload an image of the question, and I'll analyze it for you! π
In the meantime, here are some common tests for determining the interval of convergence:
- Ratio Test β Used when factorials or exponentials are involved.
- Root Test β Useful when terms have nth powers.
- Alternating Series Test β Checks convergence of alternating series.
- p-Series Test β Applies to series of the form .
- Direct Comparison Test β Compares a given series to a known convergent/divergent series.
πΉ Tip: Always check for absolute convergence and test the endpoints separately!
Let me know the series, and I'll solve it with a different test. π
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Math Problem Analysis
Mathematical Concepts
Series Convergence
Interval of Convergence
Convergence Tests
Formulas
Ratio Test: lim (nββ) |a_(n+1) / a_n|
Root Test: lim (nββ) nth-root(|a_n|)
Alternating Series Test: If decreasing and lim (nββ) a_n = 0, then convergent
Theorems
Ratio Test Theorem
Root Test Theorem
Alternating Series Theorem
Comparison Test Theorem
Suitable Grade Level
Undergraduate (Calculus II)