Sums and Products

Apuntes

Sums and Products Sums and Products Titu Andreescu Marian Tetiva Library of Congress Control Number: 2018900205 ISBN-10: 0—9993428—1-9 ISBN-13: 978-0-9993428-1-7 © 2018 XYZ Press, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (XYZ Press, LLC, 3425 Neiman Rd., Plano, TX 75025, USA) and the authors except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of tradenames, trademarks, service marks and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. 9 8 7 6 5 4 3 2 1 www.awesomemath.org Cover design by Iury Ulzutuev Contents Introduction 1 Telescoping Sums and Products in Algebra Telescoping Sums and Products in Trigonometry Complex Numbers and de Moivre’s Formula The Abel Summation Formula Mathematical Induction Combinatorial ...