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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
Is the series
∑
n
=
2
∞
(
−
1
)
n
+
1
n
2
n
3
+
3
\sum\limits^\infty_{n=2}(-1)^{n+1}\frac{n^2}{n^3+3}
n
=
2
∑
∞
(
−
1
)
n
+
1
n
3
+
3
n
2
convergent or divergent?
Converges conditionally
Converges absolutely
Diverges
Cannot be determined
I don't know
Check Submission
More Absolute Convergence & Alternating Series Test Questions:
Practice Problem
Determine whether the following series are absolutely convergent, conditionally convergent, or divergent:
a.)
∑
n
=
1
∞
(
−
1
)
n
n
\sum\limits^\infty_{n=1}\frac{(-1)^n}{n}
n
=
1
∑
∞
n
(
−
1
)
n
b.)
∑
n
=
0
∞
(
−
2
)
n
\sum\limits^\infty_{n=0}(-2)^n
n
=
0
∑
∞
(
−
2
)
n
Practice: Alternating Series Test
Is the series
∑
n
=
2
∞
(
−
1
)
n
+
1
n
2
n
3
+
3
\sum\limits^\infty_{n=2}(-1)^{n+1}\frac{n^2}{n^3+3}
n
=
2
∑
∞
(
−
1
)
n
+
1
n
3
+
3
n
2
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
)
n
n
\sum\limits^\infty_{n=1}\frac{(-1)^n}{n}
n
=
1
∑
∞
n
(
−
1
)
n
Practice: Alternating Series Test
Practice: AST
Is the series
∑
n
=
2
∞
(
−
1
)
n
+
1
n
2
n
3
+
3
\sum\limits^\infty_{n=2}(-1)^{n+1}\frac{n^2}{n^3+3}
n
=
2
∑
∞
(
−
1
)
n
+
1
n
3
+
3
n
2
convergent or divergent?
Practice: Alternating Series Test
Practice: AST
Is the series
∑
n
=
2
∞
(
−
1
)
n
+
1
n
2
n
3
+
3
\sum\limits^\infty_{n=2}(-1)^{n+1}\frac{n^2}{n^3+3}
n
=
2
∑
∞
(
−
1
)
n
+
1
n
3
+
3
n
2
convergent or divergent?
Practice: Alternating Series Test
Practice: AST
Is the series
∑
n
=
2
∞
(
−
1
)
n
+
1
n
2
n
3
+
3
\sum\limits^\infty_{n=2}(-1)^{n+1}\frac{n^2}{n^3+3}
n
=
2
∑
∞
(
−
1
)
n
+
1
n
3
+
3
n
2
convergent or divergent?
Practice: Alternating Series Test
Practice: AST
Is the series
∑
n
=
2
∞
(
−
1
)
n
+
1
n
2
n
3
+
3
\sum\limits^\infty_{n=2}(-1)^{n+1}\frac{n^2}{n^3+3}
n
=
2
∑
∞
(
−
1
)
n
+
1
n
3
+
3
n
2
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
)
n
n
\sum\limits^\infty_{n=1}\frac{(-1)^n}{n}
n
=
1
∑
∞
n
(
−
1
)
n
Practice: Alternating Series Test
Is the series
∑
n
=
2
∞
(
−
1
)
n
+
1
n
2
n
3
+
3
\sum\limits^\infty_{n=2}(-1)^{n+1}\frac{n^2}{n^3+3}
n
=
2
∑
∞
(
−
1
)
n
+
1
n
3
+
3
n
2
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
+
1
n
2
n
3
+
3
\sum\limits^\infty_{n=2}(-1)^{n+1}\frac{n^2}{n^3+3}
n
=
2
∑
∞
(
−
1
)
n
+
1
n
3
+
3
n
2
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
)
n
n
\sum\limits^\infty_{n=1}\frac{(-1)^n}{n}
n
=
1
∑
∞
n
(
−
1
)
n