Web6 n + 1 7 −n. Determine whether the geometric series is convergent or divergent. Justify your answer. Converges; the series is a constant multiple of a geometric series.Converges; the limit of the terms, a n, is 0 as n goes to infinity. Diverges; the limit of the terms, a n, is not 0 as n goes to infinity.Diverges; the series is a constant multiple of … WebMar 7, 2024 · Here we show how to use the convergence or divergence of these series to prove convergence or divergence for other series, using a method called the …
Math 116 — Practice for Exam 2 - University of Michigan
WebFinal answer. Transcribed image text: 1. Determine if each series converges or diverges. Explain any reasoning and show appropriate work for any test you use. n=1∑∞ (−1)n−1ne−3n n=1∑∞ n!e3n n=1∑∞ n2sin( 6nπ) Previous question Next question. WebQuestion #6 – Determine if the series below converges or diverges. Make sure to state what test you are using and why it works.! 2kk k = 1. Question #7 – Determine if this … dancing shrimp gif
Worked example: sequence convergence/divergence
Web1 Answer. Take f ( x) = log log x, then g ( x) = x log x. The sum of 1 / g diverges, so the sum of f / g also diverges. But f ′ / g ′ is slightly smaller than. and this sum converges. For this, you need to notice that an antiderivative of 1 x log x is log log x, while an antiderivative of 1 x ( log x) 2 is − 1 log x. WebThe series converges because ! dx = x in ² х 2 (Type an exact answer.) 7 OB. The series diverges because dx = x In ²x 2 (Type an exact answer.) OC. The Integral Test cannot be used since one or more of the conditions for the Integral Test is not satisfied. Use the Integral Test to determine if the series shown below converges or diverges. WebOct 18, 2024 · Example \( \PageIndex{3}\): Determining Convergence or Divergence of a Geometric Series. Determine whether each of the following geometric series converges or diverges, and if it converges, find its sum. \(\displaystyle \sum^∞_{n=1}\frac{(−3)^{n+1}}{4^{n−1}}\) ... a series converges if the sequence of … birkenstock oiled leather big buckle