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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) ...Show synopsisThis historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1903 edition. Excerpt: ...is convergent. 292. To shew that the expansion of (1 +x)n by the Binomial Theorem is convergent w/ien x 1. Let ur, ur+l represent the rth and (r + l)th terms of the expansion; then u r r "When rn+, this ratio is negative; that is, from this point the terms are alternately positive and negative when x is positive, and always of the same sign when x is negative. Now when r is infinite, Lim----= x numerically; therefore since x 1 the series is convergent if all the terms are of the same sign; and therefore a fortiori it is convergent when some of the terms are positive and some negative. Art. 283. 293. To shew that the expansion of ax in ascending powers ofyiis convergent for every value q/x. Here----=--; and therefore lam----1 whatever be the value of x; hence the series is convergent. 294. To shew that the expansion of log(l + x) in ascending powers of x is convergent when x is numerically less than 1. Here the numerical value of---=----x, which in the limit u, n n--1 is equal to x; hence the series is convergent when x is less than 1. If x=, the serf vergent. Art. 280. If x =--l, the series becomes--1--jr--Q-t--, and is divergent. Art. 290. This shews that the logarithm of zero is infinite and negative, as is otherwise evident from the equation e-"=0. 295. The results of the two following examples are important, and will be required in the course of the present chapter. Example 1. Find the limit of--=--when x is infinite. Put x = e; then logs = y__ y x e y'2 y3 1+y+i2+rs+ 1, y y' also when x is infinite y is infinite; hence the value of the fraction is zero. Example 2. Shew that when n is infinite the limit of nx"=0, when srl. Let x=, so that y 1; 2/ also let?/" = z, so that n log 2/=log z; then m.n=n = l log2 =...Hide synopsis

Description:New. 586 pages. Reprinted from 1891 edition. New 2013 edition...New. 586 pages. Reprinted from 1891 edition. New 2013 edition in PAPERBACK is SEWN PERFECT BOUND, much more durable than a standard paperback. This is a quality reprint of an old book of historical value. If the original book was printed in multiple volumes than this reprint is of only a single volume. This is an exact/strict reproduction of text, no changes has been made in respect to the original text. A lot of effort has been made to check and improve each page/scan manually for its quality of text and illustrations (if any, are in b/w). Folded illustrations, if any, are not included in the book. This is not a retyped or an ocr'd book. Index, contents, etc, if any in the original book, are included. This item is printed on demand using good quality natural shade paper. The title of the book, on the cover, is in gold lettering.

Description:Hardcover reprint of the original 1891 edition-beautifully bound...Hardcover reprint of the original 1891 edition-beautifully bound in brown cloth covers featuring titles stamped in gold, 8vo-6x9". No adjustments have been made to the original text, giving readers the full antiquarian experience. For quality purposes, all text and images are printed as black and white. This item is printed on demand. Book Information: Higher Algebra: A Sequel To Elementary Algebra For Schools. Hall, H. S. (Henry Sinclair). Indiana: Repressed Publishing LLC, 2012. Original Publishing: Higher Algebra: A Sequel To Elementary Algebra For Schools. Hall, H. S. (Henry Sinclair). London: Macmillan; New York: St. Martin's Press, 1891. Subject: Algebra.

Description:New. 596 pages. ReInk Books reprint from the 1891 edition. This...New. 596 pages. ReInk Books reprint from the 1891 edition. This paperback book is SEWN perfect bound, where the book block is actually sewn (smythe sewn/section sewn) with thread before binding which results in a more durable type of paperback binding. It can also be open wide. The pages will not fall out and will be around for a lot longer than normal paperbacks. NO changes have been made to the original text. Each page is checked manually before printing. Illustrations, Index, if any, are included in b/w. Fold-outs, if any, are not part of the book. If the original book was printed in multiple volumes than this reprint is of only a single volume. This book is printed on demand on acid-free paper. (Original publisher: London: Macmillan; New York: St. Martin's Press)

Description:New. This Elibron Classics title is a reprint of the original...New. This Elibron Classics title is a reprint of the original edition published by Macmillan and Co., Limited in London, 1907. This book is in English. This book contains 581 pages.