PPT-13.5 – Sums of Infinite Series

Objectives You should be able to Formulas The goal in this section is to find the sum of an infinite geometric series However this objective is very closely connected to the limit of an infinite sequence . BERNDT SUN KIM AND ALEXANDRU ZAHARESCU Key Words Circle problem Bessel functions Riesz sums weighted divisor sums Dirichlet series Ra manujans Lost Notebook 2000 Math Reviews Subject Classi64257cation Numbers Primary 11P21 Secondary 11M06 Abstract SUMS MEMBERS. ANDREA BUTTLE. Worked for SUMS since 2001. Have worked for 37 universities in that time from Solent to Cambridge. Reviewed timetabling at 19 universities. Wrote the SUMS good practice guide to teaching space management 2004. SERIES AND PARTIAL SUMS What if we wanted to sum up the terms of this sequence, how many terms would I have to use? 1, 2, 3, . . . 10, . . .  ? Well, we could start creating sums of a finite Series. Find sums of infinite geometric series.. Use mathematical induction to prove statements.. Objectives. infinite geometric series. converge. limit. diverge. mathematical induction. Vocabulary. In Lesson 12-4, you found partial sums of geometric series. You can also find the sums of some infinite geometric series. An . A. finite . sum of real numbers always produces a real number,. but an . infinite. sum of real numbers is not actually a real sum:. Definition: Infinite Series. An . infinite series . is an expression of the form. Section 10.1. Sequences. Section 10.2. Infinite Series. Section 10.3. The Integral Test. 10.4. Comparison Tests. Section 10.5. Absolute Convergence; The . Ratio and Root Tests. Section 10.6. Alternating . Power Series and Convergence. We have written statements like:. . But we have not talked in depth about what values of . make the identity true.. Example: Investigate whether or not . makes the sentence above true? . Chapter 12. This Slideshow was developed to accompany the textbook. Larson Algebra 2. By Larson. , R., Boswell, L., . Kanold. , T. D., & Stiff, L. . 2011 . Holt . McDougal. Some examples and diagrams are taken from the textbook.. All graphics are attributed to:. Calculus,10/E. by Howard Anton, Irl Bivens, and Stephen Davis. Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.”. Introduction. The purpose of this section is to discuss sums that contain infinitely many terms. All graphics are attributed to:. Calculus,10/E. by Howard Anton, Irl Bivens, and Stephen Davis. Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.”. Introduction. In the last section, we showed how to find the sum of a series by finding a closed form for the nth partial sum and taking its limit.. Consider the following sequence . , . , . , . ,…. Each term of this sequence is of the form .  . What happens to these terms as n gets very large? . In general, the . , for all positive r .  . Many sequences have limiting factors. M. ultiple . S. clerosis. SUMS. study@plymouth.ac.uk. . South West Contacts. :. Dr Jenny . Freeman . . 01752 588835. Esther . Fox . .  . 01752 . 587599. . . East Anglia Contacts :. A sequence or progression is an ordered set of numbers which can be generated from a rule.. General sequence terms as denoted as follows. a. 1 . – first term. . , a. 2. – second term, …, a. n. Fall 2011. Sukumar Ghosh. Sequence. A sequence is an . ordered. list of elements. . Examples of Sequence. Examples of Sequence. Examples of Sequence. Not all sequences are arithmetic or geometric sequences..