• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Infinite Summation

Extracts from this document...

Introduction

PK!J©Ðt[Content_Types].xml ¢( ´T[OÂ0~7ñ?,}5[Ác


ƒ/B"þ€®=ƒb×6m¹ý{φ#fV/K¶³ïr®ƒÑ¦RÉ

œ—F礟õHš!õ,'ïÓ—ôž$>0-˜2r²OFÃë«ÁtkÁ'ˆÖ>'ó쥞ϡb>34FJã*ðÕͨeüƒÍ€Þözw”@‡4Ôd8£'$æÂ+«P‡

Ã'ÎX?;È$;X­œf­’œôMWZt4Ó/½¬F§‰Àþ¦&¢qŵq‚zs÷§+š²”Ðö²Âܲš
u9x|•ÊZæÖ”l©Bò¼ÁZìÊ8ËcÖ÷Ò‡i"Å:f}Ï\1©[ÿ›†Ý9»‚PF€ˆ´/R»BêÓ&¤“´Q0.ÀÃÁñ(q§¬Pÿ˜ÈŽÞùØS·Ž$é@ùÓ²l÷‘Í®ø¹´Ø‚°Up‰hxÛcÔ,኷‹íá7ò£FÞ3 Í³ö<74­d¤¹

³NseUßÌ&€G+‚±¢ì@¾ßÅ:ú
NÇ¥,~Gm®ûðÿÿPK!
û¸

ß
_rels/.rels ¢( ¬’ÏJ1Æï‚ïæÞ¶Šˆ4Û‹½‰¬0&³»ÑÍ’TÛ·7

¶.´ÕCÉL¾ù}ßd±ÜØA¼sLÆ;³j

‚òÚ¸NÂsó0¹‘29Mƒw,aË–õåÅâ‰ÊåQêMH¢¨¸$¡Ï9Ü!&Õ³¥TùÀ®TZ-årŒRoÔ1Χӌ¿5 iŠ•–WúD³
eòßÚ¾mâ{¯Ö–]>0y“ÙiÖ“
[̦¸
ÅŽ³íÕc¹NH!Tð0ÑìœDcæ=̇
Ñ·•S4óÿÓÏ-gÒ”s¿¶/ŽÌ°GÙ岫U¯»cñ\Hùȧ×õÕñ“Ž¾eýÿÿPK!e
'qOword/_rels/document.xml.rels ¢( Ä\MÛF


½è0t¯%ΧTÄ›K[ ‡¢@»=²=ö:±%×RÚî¿/³m³4óòÀ^D&ÈÇÇG

G¯^ÿu9¯þH·é4


›ŠÖMµJÃnÜŸ†ã¦úõþ‡oÚj5Íý°ïÏã6Õcšª×w_õêçtîgþOÓÃé:­ø)ô©æùúm]O»‡té§õxMÿå0Þ.ýÌoÇúÚïÞõÇT›¦õíå3ª»Ož¹z³ßT·7ûàªÕýã•úˇÓ.}7îÞ_Ò0æ7êÓ…œØߎiÞT—´?õÿ|iÝú:«úóV¡’fŒçôÓömÚÍϦ¤Ë6í?¸}ª<ínã4æß¾ÿýý““=­·§!kœµ%Ëû(BÆŽH¤h}ÝrΈRV´/j½AVÄ’YŠYƒ …üãäjLIåÇd†ñ%­X'ÂÜÒ„’Æq>峚ŒP¤Lk"!oÈ´DLPÄm'ä


oQöáãˆXÖIÅ/F”&^Èâ‚HÈÁ#g2#² ÒQµ

GT…©)j ÷


y(ªjkÛ éˆ )äÙ¶hÍYªRl‹¢D$§€]$D8


Š”VH*9®ˆH±I…rK(ŠÚ<ÃY®Ëù ¥


ú©lDI4¥yþ02ágþ;Ñùï›5Ïr#rEq‡ù¾ßž_Ì•>~…̈Byja<¬nóé­GUÛ,œ`´E1”'+ŽU•NäPô‚¾¡‡bÑ°X¶@uEå÷RÛü*´l\:!¡åqÓ_´”Íg>[y.dOŸQý0B‹„@Ú8U


ؼy¡•ÖÕð4$/AÉ

Ñqd:ηRV
=0[J¼Póx¡0Ø°x!n1°“¥F·Y$oŒ*†Y!æ‹pŠ†/¯‘Y©æóª2D­Pž9'+ÔËp¿âdT•:?ÁŠE[Cy$;XÃ]Ñ|ZZ¶Ž`U[uØÉH3%twª


â=€n«›y°ÕsE3o1æ;ä7j„èÛC±FRüa턪ˆãn+ß`DÕ~ÔÂ*T±ÌŠp@«ÊO6 Û¨Q5Ž‹2pœ*wB¸I­aÀΨæ#Á~§;m;ÑF¢…UÆâfx¤

ã:¡1


o†ÑéŠòf¾má&Xá… ¼É¬pB10"Q5¡,l”ZUªæ

OBó,(pj¹`\ÿ8¡NÄ°‡òâ›HBv¹¤;`òPE’

...read more.

Middle

.š³wg @€ @`€€áb§ @€ @€æ
ÍÙ»3 @€ 0@Àp1ÈÓ @€ @€@s†‹æìÝ™ @€ `¸äi @€ @ 9ÃEsöîL€ @€
0\
ò4 @€ Ðœ€á¢9{w&@€ @€.yš @€hNÀpÑœ½; @€ @€
€<M€ @€4'`¸hÎÞ @€ @€†‹@ž&@€ @€š0\4gïÎ @€ @€À©-[¶ÌνfÓ¦M^:¾Ow:ñ=œ“ @€ @€

lÞ¼yÁÇçܺuëüs>â¢/‘' @€ @€¦¦›>Àá¸ÿ¡šÃñþ÷~v»]Ýn÷ÞÇ|_¾É¯R‡“Ý¡þô7Îé??çìÓ3Ê7οŸMƒÆùéýÍÙ§g”¯™_a>â¢ww%@€ @€†ˆøCäô‚Ò—î ªD!0‘~™ÈÚšÀDøýe"jrÈ1ð5.ƨ


G!@€ @€ð©"
»x” @€ÃÅ”à @€ @€À¾ÆÅÂ.%@€ @€ð5.Äwk @€ @`8Ÿ*2œ“W @€ @€
.@wK @€ @`8ÃÅpN^E€ @€4 `¸hÝ- @€ @€á
Ã9y @€ ЀÀt÷tKÜg½;n¬nÞY«ÖT'¯_{ŸßÇ$@€4!àÏ2M¨»ç¤
øˆ‹IoÐù¬ ï|þ]uô6ÔCñˆ:eÃqõŠ?úì

J/*Ë%0»ç+õœµkkjjê oïþÒö庥÷%@ \àÚK/®G®ZU/yÇÕ%õg™ƒ8|‡ÀІ‹¡©¼&f¶]VgŸù²zÅû¾X3³³uݧ½.zñÏÔ;?ç/MöâÞ2fê–»ï®_ÿÈßÕ·¾ñºöÚkç¿÷ÈfÄ“‚ÑÌ\W/\·®Î|åÇëÚ}ûꎽ3½{û³LÂE
.Mæ ЄÀ5Ÿ¸¸®]óºzíó[GÖŽúó·ÿÁü1Þ|ñ'korOâN:í´:uãÆzøÃ>ÿí«ã"

D€Àr
Lo¨×^ùÕÚ~õ§êíO;¡¶ÕlïŽþ,Ó£pA`ц‹E“ù4!°÷®]µnãº:vÿÍ¿üþ
kó·^Z¼¨]Û¾¼½ö4q ÷$@ F`vf¦vïÿˆ‹—>îÁóŸ*òÔÿ¸¹®ø殘|‚ 0Jµµqãúý7œ©];ïžÿsË»û³ÌÿK`ñ†‹Å›ù4 pÄÑÇÍßõ¶›·Ö£ŸÿÞz¦}Ü‘US«ÊWn ·$$pÄÚ3êCW]µÿÓC®©O¿ï-UÝ7Ö™xBýõû‚RŠB€@Óþ,Ótî?Ɇ‹InÏÙ¬ ½»«ŽüÞõêóÿ]µykwê1uÇ];«f÷îÿÿiøKX]§ÍzÈ£êœçýJ}êæËëœéoÔ[>rðÕ[ÊüXø³ŒŸî»€ÿGå}·ó#¡À§žZ;®ù½zïÚW×
—>iÿw×–?ýB¼é—ú0ÌÉ­8bíIuÆQGÕ
¡ùÄ"@`4«jê ù³ÌA¾C`Q>âbQ\^L€@SÙôÌzüÑG×Y¯ü¹Z?=U_»ô¢zÍ_ÞZ¯xÁ9û¿X§ÿ pßf÷ücu?ú×õ»kÏžmõ©·üj½eçÎú÷g?ô¾¿©I€À

˜©›o¼qÿ·ëë;Ûgêë7]_7m»±nÚ±§üYf…þ”û°øˆ‹ÃÂèMXn#|ýñ_¼±N{âÙ5Ýù×»]ðö¿«¶Ö-÷­½?ñ;ë¿ôÔzúwö’¾þ#WÕùòûKÄCÌîùJ=÷ôÇ×¥~?¹êµþ
Uç¼þoëÓ¯ñg™¡½ˆÀS[¶l™ÿ7z6mÚ´ÀÓ"@€ÀxìÝqcýÓŽ;ë¨5'ÖÉë׎×ᜆ‰˜ÙSÛ¶Ý\·ï;ªpâúºŸ

ub»tpã.àÏ2ãÞó“ÀÖ­[çã#.Æ©g!@` Àªã××Æã¾Ì
 °(©éÕuâúSõc¼˜÷EÀŸeî‹š³Ò|‹•þ3@~ @€ 0Ɔ‹1.ÇÑ @€ @€ÀJ0\¬ôŸò @€ @€10\Œq9ŽF€VšÀ7¾ñºì²Ëjvvþk‡ÏÇ¿úê«ëšk®©»ï¾{¥qÈK€ì0\øi@€ŒÀW\QsÿÒÙ»ßýîù3ÍguV]rÉ%55556çt @`t†‹ÑY» 0@àéOz{î¹õÖ·¾µ¾ûÝïÖ›Þô¦:õÔSë‚
.0\


°ó4H0\¤6+˜@c=¶^õªWÕ7¿ùÍêt:õ±}¬.¼ðÂ:ñÄ'0# @€‡CÀpq8½ pØ÷¸ÇÕùçŸ_ø‡XO~ò“ë¼óÎ;lïí @€Éz¸˜ÝsK}éóWÖΙC…ÜS·nÛV·í9ä‹

õK~nïîµmÛŽúÞïtë¶kûîƒÏz÷žÝûü¶ºëà‡ïõn3õµ+¯¬Ú±ï^û. °TU«VÕžð„ù·Ù¸qc­Y³f©oéÇ @€,0Ôpqýßü~±æAõÚ|¾n¯|•ï{æÞõÕíÿÜÓ5õ¬=«î¿æ¨zý¥ßºçÓ]ïüò{æ?Ouî‹lÍ};åiÿ«îøþ+f÷\WÏY»¶ÞÍ΃~Ìàïì®w]ð“µþízÆSNª¶~³nœYø¬U·Ô›ž{B=ðÄ
uÂqGÕÛ¶|gþí¯|ÿKëÈu¯¿èìZ}Ì£ëòoï«…Ï:Sß¾â]uòVÕ+ßÿÿÍ+ @€¡nºé¦ù¯qñЇ>´>ðÔ—¾ô¥¡¬ @€y‡‹ïí¸¬N{â¯O~ýöú?

...read more.

Conclusion


(µ…word/embeddings/Microsoft_Equation14.binPK-!Û°è;

'‡word/embeddings/Microsoft_Equation9.binPK-

!¿I


ˆˆword/media/image9.pngPK-!É0£

'¼‘word/embeddings/Microsoft_Equation8.binPK-

!?]!=ÜÜ“word/media/image4.pngPK-!–uH‹Ž

'+œword/embeddings/Microsoft_Equation3.binPK-

!zJ µ



þword/media/image3.pngPK-!…Eñ


';¬word/embeddings/Microsoft_Equation2.binPK-

!Ûz$5Ö
Ö
q®word/media/image2.pngPK-!Ûû£…o


'z¼word/embeddings/Microsoft_Equation1.binPK-!ðûÅ”A

'.¾word/embeddings/Microsoft_Equation4.binPK-

!ñýœ´¿word/media/image5.pngPK-!…ó–Û

'Äword/embeddings/Microsoft_Equation5.binPK-

!ä™ïøøTÅword/media/image8.pngPK-!dÖU™Ÿ


'Êword/embeddings/Microsoft_Equation7.binPK-

!<ûsMMcÌword/media/image7.pngPK-!9¥c=


'ããword/embeddings/Microsoft_Equation6.binPK-

!4Úêøø6åword/media/image6.pngPK-!3Êâ_

(aêword/embeddings/Microsoft_Equation16.binPK-

!ñýœ²ëword/media/image18.pngPK-!àªxÜ


(ðword/embeddings/Microsoft_Equation17.binPK-

!ôÓ´3ÓÓWñword/media/image33.pngPK-

!
ÀOMügüg^úword/media/image32.pngPK-! s¸W$6N˜Žbword/media/image31.pdfPK-!îþ

(æ˜word/embeddings/Microsoft_Equation26.binPK-

!4Úêøø7šword/media/image19.pngPK-!¦˜ˆS


(cŸword/embeddings/Microsoft_Equation25.binPK-!_[Ó=

(µ word/embeddings/Microsoft_Equation27.binPK-

!4Úêøø8¢word/media/image34.pngPK-!¨0¶


(d§word/embeddings/Microsoft_Equation28.binPK-

!±Bc¹¹¸¨word/media/image38.pngPK-

!é$ݳÅ^Å^¥±word/media/image37.pngPK-!eòC@ÃPz“ž        word/media/image36.pdfPK-!Fbg›


(•a        word/embeddings/Microsoft_Equation29.binPK-

!iÙ-šõõvc        word/media/image35.pngPK-

!™Ž¶_//Ÿ{        word/media/image29.pngPK-

!ñýœ€        word/media/image30.pngPK-

!Ûznñ66S„        word/media/image28.pngPK-

!Š¼§ÞÔ_Ô_½‰        word/media/image23.pngPK-!ŽY]¤%

(Åé        word/embeddings/Microsoft_Equation24.binPK-!ŸÛ0H

(0ë        word/embeddings/Microsoft_Equation19.binPK-

!žà
<<…ì        word/media/image21.pngPK-!Η¬


(õð        word/embeddings/Microsoft_Equation18.binPK-

!"¹æ¥ccHó        word/media/image20.pngPK-

!$k œ

        ß

word/media/image24.pngPK-!,HÏËvS—

word/media/image22.pdfPK-

!4ÚêøøÇh

word/media/image25.pngPK-!2,¢F

(óm

word/embeddings/Microsoft_Equation20.binPK-

!


#ÂWˆˆo

word/media/image27.pngPK-!ú¦*Ô


(;ˆ

word/embeddings/Microsoft_Equation23.binPK-

!øíãššŠ

word/media/image26.pngPK-!VK„


(Î’

word/embeddings/Microsoft_Equation21.binPK-!«C


ÊC

("”

word/embeddings/Microsoft_Equation22.binPK-!UCw"Þ}
«•

word/settings.xmlPK-!gØËä2s

¸š

word/styles.xmlPK-!ÃY×iÆž

word/webSettings.xmlPK-!Œàâ£x¿Ÿ

docProps/app.xmlPK-!ºŒIvŽ¡

docProps/core.xmlPK-!$S€@tj¤

word/fontTable.xmlPK””(+


¦

...read more.

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related International Baccalaureate Maths essays

  1. The purpose of this paper is to investigate an infinite summation patter where Ln(a) ...

    + 10 There is a horizontal asymptote as n approaches positive infinite (?). As n approaches positive infinite then Sn will approach positive ten. Sn approaches a horizontal asymptote when y=10. There is a y-intercept at (0,1). tn= n t(n)

  2. Mathematics (EE): Alhazen's Problem

    of Queen's Collage, managed to provide a new solution to the problem. Inspired by early mathematician Descartes, Nueman cleverly translated the billiards table geometry simply into x and y coordinates on two axes. 6 This is a method I intend to use further into my extended essay.

  1. Fishing Rod

    don't know how well that equation/function can go through the rest of the data points. Now we need to use the matrix method again to find a cubic equation that will model the specified data. A cubic equation is: ax3+bx2+cx+d, and to solve for it, the matrices will have to

  2. Infinite Summation- The Aim of this task is to investigate the sum of infinite ...

    This shows a relation between a and ?, when a equals 2 the maximum for Sn (S?) will also equal to 2. So this would mean that the domain of the function is 1?Sn?2. Another sequence of terms will be used to underline the observations from the sequence before, this will be done the exact same way as before.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work