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! 😊

In the meantime, here are some common tests for determining the interval of convergence:

  1. Ratio Test – Used when factorials or exponentials are involved.
  2. Root Test – Useful when terms have nth powers.
  3. Alternating Series Test – Checks convergence of alternating series.
  4. p-Series Test – Applies to series of the form βˆ‘1np\sum \frac{1}{n^p}.
  5. Direct Comparison Test – Compares a given series to a known convergent/divergent series.

πŸ”Ή 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. 😊

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Math Problem Analysis

Mathematical Concepts

Series Convergence
Interval of Convergence
Convergence Tests

Formulas

Ratio Test: lim (nβ†’βˆž) |a_(n+1) / a_n|
Root Test: lim (nβ†’βˆž) nth-root(|a_n|)
Alternating Series Test: If decreasing and lim (nβ†’βˆž) a_n = 0, then convergent

Theorems

Ratio Test Theorem
Root Test Theorem
Alternating Series Theorem
Comparison Test Theorem

Suitable Grade Level

Undergraduate (Calculus II)