#### Didn’t find what you are looking for? Series ### Find the radius of convergence, R, of the series. $$\sum_{n=1}^\infty\frac{(2x+9)^n}{n^2}$$ Find the interval, I, of convergence of the series.

Series ### Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the convergence or divergence of the series using other methods. $$\sum_{n=1}^\infty\frac{n^2}{(n+1)(n^2+2)}$$

Series ### Determine whether the series $$\sum a_n$$ an converges or diverges: Use the Alternating Series Test. $$\sum_{n=2}^\infty(-1)^n\frac{n}{\ln(n)}$$

Series ### Find the radius of convergence and interval of convergence of the series. $$\sum_{n=1}^\infty\frac{x^n}{n5^n}$$

Series ### Determine if the following series converges or diverges. If it is a converging geometric or telescoping series, or ca be written as one, provide what the series converges to. $$\displaystyle{\sum_{{{k}={2}}}^{\infty}}{\frac{{{k}}}{{{k}^{{3}}-{17}}}}$$

Series ### Taylor series and interval of convergence a. Use the definition of a Taylor/Maclaurin series to find the first four nonzero terms of the Taylor series for the given function centered at a. b. Write the power series using summation notation. c. Determine the interval of convergence of the series. $$f(x)=\log_3(x+1),a=0$$

Series ### Determine the first four terms of the Maclaurin series for sin 2x (a) by using the definition of Maclaurin series. (b) by replacing x by 2x in the series for sin 2x. (c) by multiplying 2 by the series for sin x by the series for cos x, because sin 2x = 2 sin x cos x

Series ### Differentiating and integrating power series Find the power series representation for g centered at 0 by differentiating or integrating the power series for ƒ (perhaps more than once). Give the interval of convergence for the resulting series. $$g(x)=-\frac{1}{(1+x)^2}\text{ using }f(x)=\frac{1}{1+x}$$

Series ### Determine the radius and interval of convergence for each of the following power series. $$\sum_{n=0}^\infty\frac{2^n(x-3)^n}{\sqrt{n+3}}$$

Series ### Use the Limit Comparison Test to determine the convergence or divergence of the series. $$\sum_{n=1}^\infty\frac{2n^2-1}{3n^5+2n+1}$$

Series ### Write out the first few terms of each series to show how the series start. Then find out the sum of the series. $$\sum_{n=0}^\infty(\frac{5}{2^n}+\frac{1}{3^n})$$

Series ### Consider the series $$\sum_{n=1}^\infty\frac{(-1)^n}{n^2}$$ a) Show the series converges or diverges using the alternating series test. b) Approximate the sum using the 4-th partial sum($$S_4$$) of the series. c) Calculate the maximum error between partial sum($$S_4$$) and the sum of the series using the remainder term portion of the alternating series test.

Series ### Use the binomial series to find the Maclaurin series for the function $$f(x)=\sqrt{1+x^3}$$

Series ### Determine the radius of convergence and the interval of convergence for each power series. $$\sum_{n=0}^\infty\sqrt{n}(x-1)^n$$

Series ### Determine whether the series converges or diverges. $$\displaystyle{\sum_{{{n}={2}}}^{\infty}}{\frac{{{1}}}{{{n}{\ln{{n}}}}}}$$

Series ### Use the Root Test to determine the convergence or divergence of the series. $$\sum_{n=1}^\infty(\frac{n}{500})^n$$

Series ### Consider the following series. $$\sum_{n=1}^\infty\frac{\sqrt{n}+4}{n^2}$$ The series is equivalent to the sum of two p-series. Find the value of p for each series. Determine whether the series is convergent or divergent.

Series ### Find the interval of convergence of the power series. $$\sum_{n=0}^\infty\frac{x^{5n}}{n!}$$

Series ### Verify that the infinite series converges. $$\displaystyle{\sum_{{{n}={0}}}^{\infty}}{\left(-{0.2}\right)}^{{n}}={1}-{0.2}+{0.04}-{0.008}+\ldots$$
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