Chapter 7: Problem 3
Determine the convergence or divergence of the series. $$ \sum_{n=1}^{\infty} \frac{(-1)^{n} n^{2}}{n^{2}+1} $$
Chapter 7: Problem 3
Determine the convergence or divergence of the series. $$ \sum_{n=1}^{\infty} \frac{(-1)^{n} n^{2}}{n^{2}+1} $$
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Get started for freeFind the sum of the convergent series. $$ \sum_{n=1}^{\infty} \frac{1}{9 n^{2}+3 n-2} $$
Find the sum of the convergent series. $$ \sum_{n=0}^{\infty}\left(\frac{1}{2}\right)^{n} $$
Writing In Exercises 89 and 90 , use a graphing utility to determine the first term that is less than 0.0001 in each of the convergent series. Note that the answers are very different. Explain how this will affect the rate at which each series converges. $$ \sum_{n=1}^{\infty} \frac{1}{n(n+1)} $$
Use a graphing utility to graph the function. Identify the horizontal asymptote of the graph and determine its relationship to the sum of the series. $$ \frac{\text { Function }}{f(x)=2\left[\frac{1-(0.8)^{x}}{1-0.8}\right]} \frac{\text { Series }}{\sum_{n=0}^{\infty} 2\left(\frac{4}{5}\right)^{n}} $$
Find the sum of the convergent series. $$ \sum_{n=0}^{\infty}\left(\frac{1}{2^{n}}-\frac{1}{3^{n}}\right) $$
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