calculus 2 series and sequences practice test

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Question 5 5. Ex 11.8.1 \(\sum_{n=0}^\infty n x^n\) (answer), Ex 11.8.2 \(\sum_{n=0}^\infty {x^n\over n! 326.4 272 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 272 272 Calculus 2. YesNo 2.(b). We will also give many of the basic facts, properties and ways we can use to manipulate a series. In the previous section, we determined the convergence or divergence of several series by . << Harmonic series and p-series. 31 terms. 68 0 obj What is the sum of all the even integers from 2 to 250? (answer), Ex 11.4.6 Approximate \(\sum_{n=1}^\infty (-1)^{n-1}{1\over n^4}\) to two decimal places. Which equation below represents a geometric sequence? /LastChar 127 Determine whether the series is convergent or divergent. (answer), Ex 11.10.10 Use a combination of Maclaurin series and algebraic manipulation to find a series centered at zero for \( xe^{-x}\). endobj (5 points) Evaluate the integral: Z 1 1 1 x2 dx = SOLUTION: The function 1/x2 is undened at x = 0, so we we must evaluate the im- proper integral as a limit. In mathematical analysis, the alternating series test is the method used to show that an alternating series is convergent when its terms (1) decrease in absolute value, and (2) approach zero in the limit. 11.E: Sequences and Series (Exercises) - Mathematics LibreTexts Note that some sections will have more problems than others and some will have more or less of a variety of problems. (answer), Ex 11.2.2 Explain why \(\sum_{n=1}^\infty {5\over 2^{1/n}+14}\) diverges. Differentiate u to find du, and integrate dv to find v. Use the formula: Evaluate the right side of this equation to solve the integral. /Filter /FlateDecode 272 816 544 489.6 544 516.8 380.8 386.2 380.8 544 516.8 707.2 516.8 516.8 435.2 489.6 In other words, a series is the sum of a sequence. (You may want to use Sage or a similar aid.) Sequences & Series in Calculus Chapter Exam - Study.com Absolute Convergence In this section we will have a brief discussion on absolute convergence and conditionally convergent and how they relate to convergence of infinite series. If youd like to view the solutions on the web go to the problem set web page, click the solution link for any problem and it will take you to the solution to that problem. 272 761.6 462.4 462.4 761.6 734 693.4 707.2 747.8 666.2 639 768.3 734 353.2 503 761.2 . << Here are a set of practice problems for the Series and Sequences chapter of the Calculus II notes. Calculus II - Sequences and Series Flashcards | Quizlet What if the interval is instead \([1,3/2]\)? /BaseFont/PSJLQR+CMEX10 /LastChar 127 Determine whether the sequence converges or diverges. endobj /Name/F5 If a geometric series begins with the following term, what would the next term be? MATH 126 Medians and Such. Good luck! Therefore the radius of convergence is R = , and the interval of convergence is ( - , ). << Parametric Equations and Polar Coordinates, 9.5 Surface Area with Parametric Equations, 9.11 Arc Length and Surface Area Revisited, 10.7 Comparison Test/Limit Comparison Test, 12.8 Tangent, Normal and Binormal Vectors, 13.3 Interpretations of Partial Derivatives, 14.1 Tangent Planes and Linear Approximations, 14.2 Gradient Vector, Tangent Planes and Normal Lines, 15.3 Double Integrals over General Regions, 15.4 Double Integrals in Polar Coordinates, 15.6 Triple Integrals in Cylindrical Coordinates, 15.7 Triple Integrals in Spherical Coordinates, 16.5 Fundamental Theorem for Line Integrals, 3.8 Nonhomogeneous Differential Equations, 4.5 Solving IVP's with Laplace Transforms, 7.2 Linear Homogeneous Differential Equations, 8.

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