Stewart Section 11.7: Strategy for Testing Series

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Stewart Section 11.7: Strategy for Testing Series 0/38
1 Infinite Sequences and Series · Level 2
\( \displaystyle\sum_{n=1}^{\infty} \dfrac{n^2 - 1}{n^3 + 1} \)
2 Infinite Sequences and Series · Level 2
\( \displaystyle\sum_{n=1}^{\infty} \dfrac{n - 1}{n^3 + 1} \)
3 Infinite Sequences and Series · Level 3
\( \displaystyle\sum_{n=1}^{\infty} (-1)^n \dfrac{n^2 - 1}{n^3 + 1} \)
4 Infinite Sequences and Series · Level 2
\( \displaystyle\sum_{n=1}^{\infty} (-1)^n \dfrac{n^2 - 1}{n^2 + 1} \)
5 Infinite Sequences and Series · Level 2
\( \displaystyle\sum_{n=1}^{\infty} \dfrac{e^n}{n^2} \)
6 Infinite Sequences and Series · Level 3
\( \displaystyle\sum_{n=1}^{\infty} \dfrac{n^{2n}}{(1 + n)^{3n}} \)
7 Infinite Sequences and Series · Level 3
\( \displaystyle\sum_{n=2}^{\infty} \dfrac{1}{n \sqrt{\ln n}} \)
8 Infinite Sequences and Series · Level 3
\( \displaystyle\sum_{n=1}^{\infty} (-1)^{n-1} \dfrac{n^4}{4^n} \)
9 Infinite Sequences and Series · Level 3
\( \displaystyle\sum_{n=0}^{\infty} (-1)^n \dfrac{\pi^{2n}}{(2n)!} \)
10 Infinite Sequences and Series · Level 3
\( \displaystyle\sum_{n=1}^{\infty} n^2 e^{-n^3} \)
11 Infinite Sequences and Series · Level 2
\( \displaystyle\sum_{n=1}^{\infty} \left(\dfrac{1}{n^3} + \dfrac{1}{3^n}\right) \)
12 Infinite Sequences and Series · Level 3
\( \displaystyle\sum_{k=1}^{\infty} \dfrac{1}{k \sqrt{k^2 + 1}} \)
13 Infinite Sequences and Series · Level 3
\( \displaystyle\sum_{n=1}^{\infty} \dfrac{3^n n^2}{n!} \)
14 Infinite Sequences and Series · Level 3
\( \displaystyle\sum_{n=1}^{\infty} \dfrac{\sin 2n}{1 + 2^n} \)
15 Infinite Sequences and Series · Level 3
\( \displaystyle\sum_{k=1}^{\infty} \dfrac{2^{k-1} 3^{k+1}}{k^k} \)
16 Infinite Sequences and Series · Level 3
\( \displaystyle\sum_{n=1}^{\infty} \dfrac{\sqrt{n^4 + 1}}{n^3 + n} \)
17 Infinite Sequences and Series · Level 4
\( \displaystyle\sum_{n=1}^{\infty} \dfrac{1 \cdot 3 \cdot 5 \cdot \cdots \cdot (2n - 1)}{2 \cdot 5 \cdot 8 \cdot \cdots \cdot (3n - 1)} \)
18 Infinite Sequences and Series · Level 3
\( \displaystyle\sum_{n=2}^{\infty} \dfrac{(-1)^{n-1}}{\sqrt{n} - 1} \)
19 Infinite Sequences and Series · Level 3
\( \displaystyle\sum_{n=1}^{\infty} (-1)^n \dfrac{\ln n}{\sqrt{n}} \)
20 Infinite Sequences and Series · Level 3
\( \displaystyle\sum_{k=1}^{\infty} \dfrac{\sqrt[3]{k} - 1}{k (\sqrt{k} + 1)} \)
21 Infinite Sequences and Series · Level 3
\( \displaystyle\sum_{n=1}^{\infty} (-1)^n \cos(1 / n^2) \)
22 Infinite Sequences and Series · Level 3
\( \displaystyle\sum_{k=1}^{\infty} \dfrac{1}{2 + \sin k} \)
23 Infinite Sequences and Series · Level 3
\( \displaystyle\sum_{n=1}^{\infty} \tan\left(\dfrac{1}{n}\right) \)
24 Infinite Sequences and Series · Level 3
\( \displaystyle\sum_{n=1}^{\infty} n \sin\left(\dfrac{1}{n}\right) \)
25 Infinite Sequences and Series · Level 3
\( \displaystyle\sum_{n=1}^{\infty} \dfrac{n!}{e^{n^2}} \)
26 Infinite Sequences and Series · Level 2
\( \displaystyle\sum_{n=1}^{\infty} \dfrac{n^2 + 1}{5^n} \)
27 Infinite Sequences and Series · Level 3
\( \displaystyle\sum_{k=1}^{\infty} \dfrac{k \ln k}{(k + 1)^3} \)
28 Infinite Sequences and Series · Level 2
\( \displaystyle\sum_{n=1}^{\infty} \dfrac{e^{\dfrac{1}{n}}}{n^2} \)
29 Infinite Sequences and Series · Level 3
\( \displaystyle\sum_{n=1}^{\infty} \dfrac{(-1)^n}{\cosh n} \)
30 Infinite Sequences and Series · Level 3
\( \displaystyle\sum_{j=1}^{\infty} (-1)^j \dfrac{\sqrt{j}}{j + 5} \)
31 Infinite Sequences and Series · Level 3
\( \displaystyle\sum_{k=1}^{\infty} \dfrac{5^k}{3^k + 4^k} \)
32 Infinite Sequences and Series · Level 4
\( \displaystyle\sum_{n=1}^{\infty} \dfrac{(n!)^n}{n^{4n}} \)
33 Infinite Sequences and Series · Level 4
\( \displaystyle\sum_{n=1}^{\infty} \left(\dfrac{n}{n + 1}\right)^{n^2} \)
34 Infinite Sequences and Series · Level 3
\( \displaystyle\sum_{n=1}^{\infty} \dfrac{1}{n + n \cos^2 n} \)
35 Infinite Sequences and Series · Level 4
\( \displaystyle\sum_{n=1}^{\infty} \dfrac{1}{n^{1 + \dfrac{1}{n}}} \)
36 Infinite Sequences and Series · Level 5
\( \displaystyle\sum_{n=2}^{\infty} \dfrac{1}{(\ln n)^{\ln n}} \)
37 Infinite Sequences and Series · Level 4
\( \displaystyle\sum_{n=1}^{\infty} (\sqrt[n]{2} - 1)^n \)
38 Infinite Sequences and Series · Level 4
\( \displaystyle\sum_{n=1}^{\infty} (\sqrt[n]{2} - 1) \)

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