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Practice Problem

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Wize University Calculus 2 Textbook > Sequences and Series

Absolute Convergence & Alternating Series Test

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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}


b.) ∑n=0∞(−2)n\sum\limits^\infty_{n=0}(-2)^n



c.) ∑n=1∞(−1)nn53\sum\limits^\infty_{n=1}\frac{(-1)^n}{\sqrt[3]{n^5}}

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: 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
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}