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Practice: Alternating Series Test

Related Topics

Wize University Calculus 2 Textbook > Sequences and Series

Absolute Convergence & Alternating Series Test

4 Activities

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Mark Yourself Question
  1. Grab a piece of paper and try this problem yourself.
  2. When you're done, check the "I have answered this question" box below.
  3. View the solution and report whether you got it right or wrong.

Practice: AST

Is the series∑n=2∞(−1)n+1n2n3+3\sum\limits^\infty_{n=2}(-1)^{n+1}\frac{n^2}{n^3+3} convergent or divergent?

More Absolute Convergence & Alternating Series Test Questions:
Practice: Alternating Series Test
Is the series∑n=2∞(−1)n+1n2n3+3\sum\limits^\infty_{n=2}(-1)^{n+1}\frac{n^2}{n^3+3} convergent or divergent?
Practice Problem
Determine whether the following series are absolutely convergent, conditionally convergent, or divergent:
a.) ∑n=1∞(−1)nn\sum\limits^\infty_{n=1}\frac{(-1)^n}{n}
b.) ∑n=0∞(−2)n\sum\limits^\infty_{n=0}(-2)^n
Practice: Alternating Series Test
Is the series∑n=2∞(−1)n+1n2n3+3\sum\limits^\infty_{n=2}(-1)^{n+1}\frac{n^2}{n^3+3} convergent or divergent?
Practice Problem
Example: Absolute Convergence Test
Determine whether the following series are absolutely convergent, conditionally convergent, or divergent:
a.) ∑n=1∞(−1)nn\sum\limits^\infty_{n=1}\frac{(-1)^n}{n}
Practice: Alternating Series Test
Practice: AST
Is the series∑n=2∞(−1)n+1n2n3+3\sum\limits^\infty_{n=2}(-1)^{n+1}\frac{n^2}{n^3+3} convergent or divergent?
Practice: Alternating Series Test
Practice: AST
Is the series∑n=2∞(−1)n+1n2n3+3\sum\limits^\infty_{n=2}(-1)^{n+1}\frac{n^2}{n^3+3} convergent or divergent?
Practice: Alternating Series Test
Practice: AST
Is the series∑n=2∞(−1)n+1n2n3+3\sum\limits^\infty_{n=2}(-1)^{n+1}\frac{n^2}{n^3+3} convergent or divergent?
Practice Problem
Example: Absolute Convergence Test
Determine whether the following series are absolutely convergent, conditionally convergent, or divergent:
a.) ∑n=1∞(−1)nn\sum\limits^\infty_{n=1}\frac{(-1)^n}{n}
Practice: Alternating Series Test
Is the series∑n=2∞(−1)n+1n2n3+3\sum\limits^\infty_{n=2}(-1)^{n+1}\frac{n^2}{n^3+3} convergent or divergent? If convergent, determine whether it converges conditionally or absolutely.
Practice: Alternating Series Test
Practice: AST
Is the series∑n=2∞(−1)n+1n2n3+3\sum\limits^\infty_{n=2}(-1)^{n+1}\frac{n^2}{n^3+3} convergent or divergent?
Practice Problem
Example: Absolute Convergence Test
Determine whether the following series are absolutely convergent, conditionally convergent, or divergent:
a.) ∑n=1∞(−1)nn\sum\limits^\infty_{n=1}\frac{(-1)^n}{n}