Introduction to infinite series

/v\. i! tt.STAT.UBRAItINTRODUCTIONTOINFINITE SERIESBYF.WILLIAM Pir.D.OSGOOD,PROFESSOR OF MATHEMATICS INASSISTANT HARVARD UNIVERSITYCAMBRIDGEIbarparfcb$ "Ulniversitp1897Copyright, 1897, byUNIVERSITY.HARVARDfftfl/fftiPKEPACE.an course on the Differential and CalculusTN Integralintroductorythe of Infinite forms an TheSeriessubject important topic.of this should have in view first to make thepresentation subjectwith the nature and use of infinite series andbeginner acquaintedto introduce him to the of these series in such a waysecondly theorythat he sees at each what the at issue is andstep questionpreciselynever enters on the of a theorem till he feels that the theoremproofAids to the attainment of these ends are :actually requires proof.a of taken from the cases that arisevariety illustrations, actually(a)in of the of series to both inpractice, application computation pureand mathematics a full and careful of the;applied (b) expositionand of the more difficult theorems the use of;meaning scope (c)and illustrations in thediagrams graphical proofs.The that follows is to a ofpamphlet designed give presentationthe kind here indicated. The references are to sByerly Differentialinand Problems CalculusCalculus, Integral Calculus, ,Differentialand to B. O. Peirce s Short Table allof Integrals; published byGinn & Boston.Co.,F.WM. OSGOOD.1897.CAMBRIDGE, AprilLNTKODUCTIOISr.Consider the successive values of the variable1. Example.~n2 1s ...