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Sequence and Series
5: Determine whether the alternating series converges.
\sum_{n=1}^{\infty}(-1)^{n+1} \frac{1}{n^{2}}
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Sequence and Series
Example 5: Show that the ratio test is inconclusive for the following series. Then use another method to determine the convergence or divergences of the series.
\sum_{n=1}^{\infty} \frac{n^{2}+1}{(n+1)^{2}}
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Sequence and Series
\sum_{n=1}^{\infty} \frac{n^{2}-4}{2^{n}}
Use the ratio test to determine whether the series converges or diverges.
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Sequence and Series
Example 3: Use any test covered in 11.1-11.6 to determine whether the following seriesconverges ordiverges.
\sum_{n=1}^{\infty} \frac{1-\sin n}{n^{3 / 2}}
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Sequence and Series
Example 2: Use the limit comparison test to determine whether the following series converges or diverges.
\sum_{n=1}^{\infty} \frac{n^{2}-2 n+5}{\sqrt{3+n^{5}}}
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Sequence and Series
Example 1: Use the comparison test to determine whether the following series converges or diverges.
\sum_{n=1}^{\infty} \frac{\ln n}{n}
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Sequence and Series
Determine the Taylor series of the given function. Find the radius of convergence.
f(x)=\cos \left(2 x^{3}\right)
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Sequence and Series
Find the power series for the given function. What is the radius of convergence?
f(x)=\frac{1}{1+3 x}
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Sequence and Series
Determine the interval of convergence for the given power series.
\sum_{n=0}^{\infty} \frac{(3 x)^{n}}{n !}
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Sequence and Series
5: Decide whether the series converges. If so, find its sum.
\sum_{n=1}^{\infty} \frac{3}{n(n+1)}
\sum_{n=2}^{\infty} \frac{3^{n}-1}{5^{n-2}}
Use the Ratio or Root test, to determine whether the series converges or diverges.
\sum_{n=1}^{\infty} \frac{(\ln n)^{2 n}}{n^{n+1}}
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