Ex 11.5.1 \(\sum_{n=1}^\infty {1\over 2n^2+3n+5} \) (answer), Ex 11.5.2 \(\sum_{n=2}^\infty {1\over 2n^2+3n-5} \) (answer), Ex 11.5.3 \(\sum_{n=1}^\infty {1\over 2n^2-3n-5} \) (answer), Ex 11.5.4 \(\sum_{n=1}^\infty {3n+4\over 2n^2+3n+5} \) (answer), Ex 11.5.5 \(\sum_{n=1}^\infty {3n^2+4\over 2n^2+3n+5} \) (answer), Ex 11.5.6 \(\sum_{n=1}^\infty {\ln n\over n}\) (answer), Ex 11.5.7 \(\sum_{n=1}^\infty {\ln n\over n^3}\) (answer), Ex 11.5.8 \(\sum_{n=2}^\infty {1\over \ln n}\) (answer), Ex 11.5.9 \(\sum_{n=1}^\infty {3^n\over 2^n+5^n}\) (answer), Ex 11.5.10 \(\sum_{n=1}^\infty {3^n\over 2^n+3^n}\) (answer). If the series is an alternating series, determine whether it converges absolutely, converges conditionally, or diverges. A proof of the Integral Test is also given. This will work for a much wider variety of function than the method discussed in the previous section at the expense of some often unpleasant work. )^2\over n^n}(x-2)^n\) (answer), Ex 11.8.6 \(\sum_{n=1}^\infty {(x+5)^n\over n(n+1)}\) (answer), Ex 11.9.1 Find a series representation for \(\ln 2\). Chapters include Linear 665 570.8 924.4 812.6 568.1 670.2 380.8 380.8 380.8 979.2 979.2 410.9 514 416.3 421.4 6.5E: Exercises for Comparison Test - Mathematics LibreTexts More on Sequences In this section we will continue examining sequences. Strategy for Series In this section we give a general set of guidelines for determining which test to use in determining if an infinite series will converge or diverge. Solution. /LastChar 127 272 761.6 462.4 462.4 761.6 734 693.4 707.2 747.8 666.2 639 768.3 734 353.2 503 761.2 x=S0 ZrNRG{I~(iw%0W5b)8*^ yyCCy~Cg{C&BPsTxp%p Power Series In this section we will give the definition of the power series as well as the definition of the radius of convergence and interval of convergence for a power series. /Name/F6 590.3 767.4 795.8 795.8 1091 795.8 795.8 649.3 295.1 531.3 295.1 531.3 295.1 295.1 The Alternating Series Test can be used only if the terms of the series alternate in sign. /Filter /FlateDecode 979.2 489.6 489.6 489.6] PDF Arithmetic Sequences And Series Practice Problems /LastChar 127 500 388.9 388.9 277.8 500 500 611.1 500 277.8 833.3 750 833.3 416.7 666.7 666.7 777.8 (answer). |: The Ratio Test shows us that regardless of the choice of x, the series converges. /FontDescriptor 20 0 R A Lot of Series Test Practice Problems - YouTube /Type/Font A review of all series tests. Sequences In this section we define just what we mean by sequence in a math class and give the basic notation we will use with them. 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 (answer). The practice tests are composed In the previous section, we determined the convergence or divergence of several series by . 207 0 obj <> endobj stream I have not learned series solutions nor special functions which I see is the next step in this chapter) Linear Algebra (self-taught from Hoffman and Kunze. MATH 126 Medians and Such. (answer), Ex 11.2.3 Explain why \(\sum_{n=1}^\infty {3\over n}\) diverges. 68 0 obj in calculus coursesincluding Calculus, Calculus II, Calculus III, AP Calculus and Precalculus. 26 0 obj /LastChar 127 Calculus II - Series - The Basics (Practice Problems) - Lamar University Ex 11.1.2 Use the squeeze theorem to show that \(\lim_{n\to\infty} {n!\over n^n}=0\). S.QBt'(d|/"XH4!qbnEriHX)Gs2qN/G jq8$$< These are homework exercises to accompany David Guichard's "General Calculus" Textmap. The Ratio Test can be used on any series, but unfortunately will not always yield a conclusive answer as to whether a series will converge absolutely or diverge. We will also give the Divergence Test for series in this section. Worked example: sequence convergence/divergence, Partial sums: formula for nth term from partial sum, Partial sums: term value from partial sum, Worked example: convergent geometric series, Worked example: divergent geometric series, Infinite geometric series word problem: bouncing ball, Infinite geometric series word problem: repeating decimal, Proof of infinite geometric series formula, Convergent & divergent geometric series (with manipulation), Level up on the above skills and collect up to 320 Mastery points, Determine absolute or conditional convergence, Level up on the above skills and collect up to 640 Mastery points, Worked example: alternating series remainder, Taylor & Maclaurin polynomials intro (part 1), Taylor & Maclaurin polynomials intro (part 2), Worked example: coefficient in Maclaurin polynomial, Worked example: coefficient in Taylor polynomial, Visualizing Taylor polynomial approximations, Worked example: estimating sin(0.4) using Lagrange error bound, Worked example: estimating e using Lagrange error bound, Worked example: cosine function from power series, Worked example: recognizing function from Taylor series, Maclaurin series of sin(x), cos(x), and e, Finding function from power series by integrating, Integrals & derivatives of functions with known power series, Interval of convergence for derivative and integral, Converting explicit series terms to summation notation, Converting explicit series terms to summation notation (n 2), Formal definition for limit of a sequence, Proving a sequence converges using the formal definition, Infinite geometric series formula intuition, Proof of infinite geometric series as a limit. /Length 200 /Widths[611.8 816 761.6 679.6 652.8 734 707.2 761.6 707.2 761.6 707.2 571.2 544 544 /Type/Font If you . raVQ1CKD3` rO:H\hL[+?zWl'oDpP% bhR5f7RN `1= SJt{p9kp5,W+Y.e7) Zy\BP>+``;qI^%$x=%f0+!.=Q7HgbjfCVws,NL)%"pcS^ {tY}vf~T{oFe{nB\bItw$nku#pehXWn8;ZW]/v_nF787nl{ y/@U581$&DN>+gt
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