MATH1051 Lecture Notes - Lecture 22: Ratio Test, Absolute Convergence, Root Test

estion. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the qu Determine if the series converges absolutely, converges, or diverges. 1) 5n3 + 6 A) Converges absolutely B) Diverges C) Converges conditionally Use the Ratio Test to determine if the series converges or diverges 2) A) Converges B) Diverges Find the Maclaurin series for the given function. 3) 3) e9x A) B) n! n! n=0 n! Find the Taylor polynomial of order 3 generated by f at a. 4) 4) f)-+10 a o 1xx2 3 A) P3-0 100 100 0 B) P3() 1010 1000 10,000 x x2 x3x4 x x2 x3 100 7000 10.00 D) P3(x) =-10 + 100 1000 10,000 Use the nth-Term Test for divergence to show that the series is divergent, or state that the test is inconclusive. 5) 5) n +4 n=1 B) diverges C) inconclusive D) converges. 4 A) converges, 4 Use the Root Test to determine if the series converges or diverges. 6) In n 3n +4 A) Converges n-1 B) Diverges C-1

points SEssCalcET2 8.4.010 MI My Notes : A st the series for convergence or divergence. (-1)P n=1 Identify bn Evaluate the following limit lim bn Since ninno bn ? ▼ 0 and bn + 1 ? ▼ bn for all n. ..-Select-" If the series is convergent, use the Alternating Series Estimation Theorem to determine how many terms we need to add in order to find the sum with an error less than 0.0001? (If the quantity diverges, enter DIVERGES.) terms Need Help?

Consider the series an where an = 9n/(7n2 + 2)6n+4 In this problem you must attempt to use the Ratio Test to decide whether the series converges. Compute L = an+1/an Enter the numerical value of the limit L if it converges, INF if it diverges to infinity, MINF if it diverges to negative infinity, or DIV if it diverges but not to infinity or negative infinity. L = Which of the following statements is true? The Ratio Test says that the series converges absolutely. The Ratio Test says that the series diverges. The Ratio Test says that the series converges conditionally. The Ratio Test is inconclusive, but the series converges absolutely by another test or tests. The Ratio Test is inconclusive, but the series diverges by another test or tests. The Ratio Test is inconclusive, but the series converges conditionally by another test or tests. Enter the letter for your choice here: For each of the series below select the letter from a to c that best applies and the letter from d to k that best applies. A possible answer is af, for example. The series is absolutely convergent. The series converges, but not absolutely. The series diverges. The alternating series test shows the series converges. The series is a \(p\)-series. The series is a geometric series. We can decide whether this series converges by comparison with a \(p\) series. We can decide whether this series converges by comparison with a geometric series. Partial sums of the series telescope. The terms of the series do not have limit zero. None of the above reasons applies to the convergence or divergence of the series. cos(n pi)/n pi 4+sin(n)/ cos2(n pi)/ni 1/nlog(4 + n) (2n + 7)!/(n!)2 1/n