![]() ![]() “Private tutoring and its impact on students' academic achievement, formal schooling, and educational inequality in Korea.” Unpublished doctoral thesis. Tutors, instructors, experts, educators, and other professionals on the platform are independent contractors, who use their own styles, methods, and materials and create their own lesson plans based upon their experience, professional judgment, and the learners with whom they engage. Varsity Tutors connects learners with a variety of experts and professionals. Varsity Tutors does not have affiliation with universities mentioned on its website. Media outlet trademarks are owned by the respective media outlets and are not affiliated with Varsity Tutors.Īward-Winning claim based on CBS Local and Houston Press awards. Names of standardized tests are owned by the trademark holders and are not affiliated with Varsity Tutors LLC.Ĥ.9/5.0 Satisfaction Rating based upon cumulative historical session ratings through 12/31/20. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License. We recommend using aĪuthors: Gilbert Strang, Edwin “Jed” Herman Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses theĬreative Commons Attribution-NonCommercial-ShareAlike License In each case, find the minimum value of N N such that the N th N th partial sum of the series accurately approximates the left-hand side to the given number of decimal places, and give the desired approximate value. Use this expression to compute the maximum overhang (the position of the edge of the top block over the edge of the bottom block.) See the following figure.Įach of the following infinite series converges to the given multiple of π π or 1 / π. ![]() This implies that ( N − 1 ) x = ( 1 2 − x ) ( N − 1 ) x = ( 1 2 − x ) or x = 1 / ( 2 N ). Let x x denote the position of the edge of the bottom block, and think of its position as relative to the center of the next-to-bottom block. Archimedes’ law of the lever implies that the stack of N N blocks is stable as long as the center of mass of the top ( N − 1 ) ( N − 1 ) blocks lies at the edge of the bottom block. Suppose that N N equal uniform rectangular blocks are stacked one on top of the other, allowing for some overhang. We can find the sum of all finite geometric series. , where a1 a 1 is the first term and r r is the common ratio. The general form of the infinite geometric series is a1 + a1r +a1r2 + a1r3 +. ![]()
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