/Length 1274 /Height 53 /Height 87 /Length 2364 0 /Subtype /Image % 'FormXob.fea33bb763dc1c10f6f75ceab4a51840': class PDFImageXObject /Height 33 Gb"/c_$U/b#XeRjO-\(fBN'h`G#\/^$Y'):7%.kqC.\f`SL:[6ZL&*b?/l,EKO%)3To,mDSkMGNR(qOg=^=>1Y,a8#\A-DandQS?a_nN2V#s_+b~>endstream 527.9469 ] endobj /Rect [ 126.0507 /Filter [ /ASCII85Decode /Filter [ /ASCII85Decode Laboratories: GEOM. /Subtype /Image /Width 663 >> << /A << /S /URI /Filter [ /ASCII85Decode Gb"/b8Ig8)$j6D,7n6*h6%u2h9G)N0#Uc2Z6jOrcU$\q!nJq3"2Y?r+KtcqB3/Bcrr/*B:Ra&36`cWiKgZRNre&(3d?.jZFiF:Z\qfK)+G/XOXQg/lVWH5Vt[Q^]'YMX*`1AWU`MjJIM7k1c11M%tJ;endstream endobj /Text /Height 100 55 0 obj 339.3469 ] /Parent 109 0 R endobj /ImageC /FlateDecode ] :8o6fF4s?~>endstream /ColorSpace /DeviceRGB /Height 90 Was studied in depth by Euler and others before Riemann. \sum_{n=1}^{\infty} \left(\dfrac{1}{n} - \dfrac{1}{n-\frac{1}{2}}\right) /URI (http://en.wikipedia.org/w/index.php?title=Harmonic_series_%28mathematics%29) >> /Subtype /Image /Subtype /Image /Subtype /Image /Length 872 /Type /Annot >> 54 0 obj << /BitsPerComponent 8 /Border [ 0 /FlateDecode ] /Width 663 >> /Subtype /Image /Height 87 /FormXob.11b7770984f92ff1d192318027a90f81 13 0 R /FormXob.768ddd1761b2e6ac606e831dbf974e72 32 0 R /ColorSpace /DeviceRGB /ColorSpace /DeviceRGB endobj /Type /Action 44 0 obj /FormXob.3a258cec0cf1971f06f307934fea933a 22 0 R /ColorSpace /DeviceRGB !=Y$_\dds2!5M!Gqa9r5!Aq)d*/-9E4m(e+*HM.FTHK7[C.9\#>O>!WrEFhg3n_Jno+rL%e:'H?K.OQ?%)s<2Q`uA7fT!7h0rf7:mmScaBnHl@r!A6QOj;B"fHF;c>l#k`[MP1TsO@X)!4Lphj##[\AthaNW.uNu\#WMTj<1GZe=XPT,)9=L*s'72oTrRAhVW3V:E.R@2b=Qdt34FF, LZ]?KR++55?VDSAp^'A8_hLkB&F(FcZ)Rj:1mW_/%2>5NDe1@GSe-IH]*VC#P=^t#T6HrCc^#F^1S#1Kto=ub=ub8;t@'Y&QMa(?DRL`&drln=*+N"ogA>E51CmEe/!/MN.8-@,**Z[$u>:VHT=@Z.s0.OHV9RW]*X>Lg@op=V/lCm8!`[;/Rkq)S?MMmGD8%+o%PYPrU$I"6\PI7:mhRU4#S\Uuse'd^_\`Ob)f+=;S*@K$+%6Tj8SJ:Fh>L"=-:2P,FcuDroC>bF@'j#1N4O+1.=BZ>Zb`j"c8-ODF0F!.3&-I7di%@\45U9#C5X3I#5Wm725S$Nqzzz!1^oUZ`lr]~>endstream /Width 703 >> stream Funcția zeta Riemann ζ(s) este o funcție de variabilă complexă s inițial definită prin următoarea serie infinită: () = ∑ = ∞pentru anumite valori ale lui s și apoi continuată analitic la toate numerele complexe s ≠ 1. /ColorSpace /DeviceRGB 0 /Width 50 >> << /A << /S /URI /Length 746 /ColorSpace /DeviceRGB 527.9469 ] /Border [ 0 /Height 87 << /A << /S /URI 46 0 obj /FlateDecode ] << /BitsPerComponent 8 /FlateDecode ] /Type /XObject /ColorSpace /DeviceRGB /ColorSpace /DeviceRGB /ColorSpace /DeviceRGB &= -2 \ln(2) \\ 0 ] /Height 50 /Filter [ /ASCII85Decode Gb"0Vd?<6D$q*tks$s+f[8WK<9ac\lM@dAfGt^%1RqrC+[^,c?!!"-ZqbQl7Y!kehACTP!0ua]2^$W#gKj9Fm)TX=7HVhDA)XIG>gBQ1YRZECGa=(F)W0]6Y%Ucu:XV33+))[LQ^em@nN%oJU-ls6`OAUWt`Y^df&e;l*UBWJgE6&l+#>i:2G\#;h7L]hFA*a1f3#%F4)T\kn+_-HO5RE5*O\l2u2)o-*YlcE5:cpLJ+JT-rN%oJU,ohe47L`nXi/f\5%\SJBn]7Y[N#EZk`n1iITm1+t5Xl1m).W"58iRNGN#Kd9_'*A(?bcXA:rV>$!!".#s1AC5J@qfUcF?@ccim]47fc)>r>+Q7Z;]T;&+1==3XTm&`XpXKh<<9kTZU,c[%G&SbL3M?Ka,;gEK6H_lW5r:H+K8H4`]fC=8FIOD$S">!5IOa83VR=Pg\[>Z$Y-IS$6hN\*NK(nAdKk"jZPXa6DTAoem.mA83@E/u<6"ZY5#WIhUt:a(7oT_U0duT'Od&U3sbc=6f/f("U&9uol,8SHAutK\R]/e_tS#Q6Q@iKEH>Sbig!O`kO8`;Jn`s@hAs+kDT`]``]m"l+%.)h-fT+oDd\'DMH^7)J?Qm!?/EK;%OH_85BP`j%t:C;kss*!KN'43L;iuWE>pRj8/IrlbGN;N-#eVpU4*gq8_P5BmNoNJVMWd!q>dah/d^`kCZ53'. endobj Riemann Surfaces por Simon Donaldson, 9780199606740, disponible en Book Depository con envío gratis. /Type /XObject /Height 103 /Subtype /Image Consider a sequence x1,x2,x3,x4,…,x_{1}, x_{2}, x_{3}, x_{4}, \ldots,x1​,x2​,x3​,x4​,…, and let Sn=x1+x2+x3+⋯+xn.S_{n} = x_{1}+ x_{2} + x_{3} + \cdots + x_{n}.Sn​=x1​+x2​+x3​+⋯+xn​. endobj /ColorSpace /DeviceRGB /FormXob.ca9029b6f90433848c770746e7b0733b 49 0 R /Filter [ /ASCII85Decode /Subtype /Link % 'FormXob.92ec843de631dccd713578c1a32ce36a': class PDFImageXObject % 'FormXob.768ddd1761b2e6ac606e831dbf974e72': class PDFImageXObject https://brilliant.org/wiki/riemann-series-theorem/. << /Annots [ 2 0 R /Type /Action << /BitsPerComponent 8 The given series is actually an infinite harmonic series. Riemann sums is the name of a family of methods we can use to approximate the area under a curve. /Subtype /Image /Height 90 /Width 233 >> Forgot password? 54 0 obj /Filter [ /ASCII85Decode << /BitsPerComponent 8 /Width 107 >> /Subtype /Image << /BitsPerComponent 8 /Filter [ /ASCII85Decode 59 0 obj /FormXob.fcf2cb3237f643587da6111047259884 40 0 R /Type /XObject 55 0 obj % 'Annot.NUMBER15': class PDFDictionary endobj /Border [ 0 stream endobj )L5C`9=u!WYJendstream Math. stream /Filter [ /ASCII85Decode 784.9469 ] )FF3nf)gs3jX.uFB2[JrBPQER`_t>]8D!9!WW3#zzzzzzn3[,(NW9%ZeNX#@3ZJ,"JG].YXH!Pd!8u_(XT/>$g,W@endstream << /BitsPerComponent 8 /Filter [ /ASCII85Decode ]f/8;])/+7qC7i;!1K1pPigSOGujA3",f]9PL]W-f`*TaS,9r.`A/b$TdIsJ;QV[On!8qV2RpZhEBdiVfDqWX6pM$(6/#hWn0=fC.sg)PgAQ4Nq*5Fo\27pj%$icjendstream 0 /Subtype /Image /Length 199 /Rect [ 360.3674 339.3469 ] /Width 1063 >> /Length 746 /FlateDecode ] % 'Annot.NUMBER18': class PDFDictionary 55 0 obj << /A << /S /URI endobj /Width 233 >> /Subtype /Image /Width 83 >> L'aire correspondant à la somme de la série est indiquée en jaune. /Rect [ 94.91291 /FlateDecode ] 0 Les séries de Riemann ne sont autre que les séries des suites de Riemann, des suites de la forme : 1. u n = 1 n r {\displaystyle u_{n}={\frac {1}{n^{r}}}} Le coefficient r est appelé la raison de la suite, par analogie avec les suites géométriques. 38 0 obj 0 /Subtype /Link endobj /FormXob.ef915955cd1d900e291dcfbe99b236eb 31 0 R /FlateDecode ] But why? 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For the understanding of this writing, the reader should have some notions, as they are it: function analytic, sequential expansion of Taylor, series of Laurent, among others.La llamada función Zeta de Riemann fue introducida por Euler, que se trata de una serie convergente en la que z es un número complejo con parte real mayor que uno. /Height 53 55 0 obj /Filter [ /ASCII85Decode /Width 30 >> /ColorSpace /DeviceRGB % 'Annot.NUMBER10': class PDFDictionary << /BitsPerComponent 8 /ColorSpace /DeviceRGB /Width 50 >> /FormXob.ef915955cd1d900e291dcfbe99b236eb 31 0 R /Type /XObject Riemann series theorem 1 Riemann series theorem In mathematics, the Riemann series theorem (also called the Riemann rearrangement theorem), named after 19th-century German mathematician Bernhard Riemann, says that if an infinite series is conditionally convergent, then its terms can be arranged in a permutation so that the series converges to any given value, or even diverges. /Border [ 0 3 0 R /Type /Action /FlateDecode ] /URI (http://en.wikipedia.org/w/index.php?title=Positive_integer) >> 175.3229 /Length 199 /Text /Subtype /Link % 'FormXob.aa11c21b9113bc000b1bd4cf119b3c27': class PDFImageXObject /FormXob.fcf2cb3237f643587da6111047259884 40 0 R /Subtype /Image /Type /Action /Subtype /Image /Type /XObject 23 0 obj << /Annots [ 37 0 R Gb"/igQ$n?$jHJ,O,j'5#uQj&(LQ3mH.o),4s"0:]%\,'lZ%jpY2"f+PG+NG3#iQ+R'&>k3:$MiO>GLs6*p-\AN%j4@[ho$H.9^$:^A6G9H9lB7]u-+T7=1S2;ZN/[KZ[IPLF@=W"$:fnS;;hAfE2*RzE1e;h9SmXm#7-Q(h-+iS.S5"kgIe,EGM*sN`GjZTo`V]GLScAf@sALS[A%@Ak7#W;>Co)lWOKFm-F=':n'L_)B9d[SePbkWPLoM72dT0#JR*Jh3:mned\1A^&?'aN_@HMJk&I>_c(Uo&%W>c^-hM+#S%r0iZiXGYLI?m)"GSn3X(SrV"Q9D(9.(P.U)ie.HD^NH#aCP1hC8T%lIHL`')t&.flgm#J.Oe]peiSmiV&'Ea"Op^mMQ6TZ.HRX7f8]#nc^l[sX35<=$cM"OM'LjQgY;'pF_Gi]n*P[um)V,oM-Pd!6YK5+"=,X"PVp[`=KO.`]5Z9Ye=qKN!%^7d2*651(m>gORG^_ZIt9! << /BitsPerComponent 8 /FlateDecode ] /Length 390 /Width 47 >> /Type /XObject Biografie. Record appears in: /ColorSpace /DeviceRGB /Width 1140 >> << /BitsPerComponent 8 /Type /Annot >> /Width 353 >> /URI (http://en.wikipedia.org/w/index.php?title=Bernhard_Riemann) >> endobj So we can say that lim⁡n→∞∑n=1∞xn=S\lim_{n \rightarrow \infty} \sum_{n=1}^{\infty} x_{n} = Slimn→∞​∑n=1∞​xn​=S. % 'Page2': class PDFPage << /BitsPerComponent 8 << /A << /S /URI /Contents 110 0 R /Length 4596 /FlateDecode ] /Height 100 /Length 1900 /Type /XObject stream /Filter [ /ASCII85Decode /Filter [ /ASCII85Decode /Filter [ /ASCII85Decode << /A << /S /URI Gb"0Th2X!9%RB!cs$K:$S^s%2P:H&T(g,\OFAp0r"+@W?r<<6%!!&[Xf7.CF!MlL@JIBL!!&36ps(3V[,^Om+SI7+h`rQ/ofB^KDN.?/fI86j'=q=$@%VN#[/7YE#\iX(%n>W<2nJ-pO^E!TVf\8WDf!#=uEi=N@WE8`bV!%Qni_BET8i50I6!*$a\KL=,O^kLeK!2tGB#`#)'JIBL!!)N^b&Iq+-!uHt"!2'DM,92;9#;-u$!'g_#7lUXR%U:t'!.YE$O)PA.*Op&.!!!c'*oR[;3cO%;!!"M,4i/@Uodp@8ktrJ,qI4+!+#<<5Pt+-F*CYH%gIl.%RXg=#cY?*VjuR$_a?e-f7q`J#Ch[;H)JBW(S1GTuKq>('[J41K'9Ci^TYVA_Ge.Kr=R>@)sSCk6srRk$5Z3)&+u`_$^7kG$SLoP9Q?l8%99**h-oc"4rC7Y`tJ/Kj4^Nli'0XhT&&fO'Iaa'nDe1o@]]A&V34HOW/%;Cber.Jk$2&-&j4G)"%T1fS-$V^VdsRZUP+5[!4^f&-(S$-1n#/`BD+CrY7M5<4!4+?%]0P"h+Ta9Re_8aBR]G!_P*4N/N)dLX`-X)E3"ppFr74dl0TK]D8lTo9Wc]fO:7)lbP&q")N,iWckN&G+b;gn&6,hCE-Km=Vpr>%]N%-21!DOo*O9kJ1Ah"#iY-AgG3o&8Wa6rb,biKg't:D241Xa38#JBPl5-O.H%:cI058SUtQa-5JbW:%l*D]Q)+1P#u'SZH17W6_tKr((qon`4)\(T^FcY*UqO[6DB%j5j6>`]-Bq"1=lX2^QH0\bc;bbuJpcHJO[:Cnfe:#*V\\3l^\deQ+*/1uPkf:lI/fAOHc_Pomhh*r.q;#@d`RGqL2?j?!NJqY2Ci;3-)o`2E%]N83N&NC^7hun9=4rj\[3_Q51mW']M;*/X$+PpcOH<5%$@c=NG/cRZ2HC.Yak9^F25c_3U[O]U$!nJlN4]eb"A\;KWa8e0@mr3qZo]^6_2g97?*eYM"H%BJt4b$7!d-b!TmF%Kil+4jp&i\aaj!USp*%PkIhlR-#b#YbNq]S$8S])ri$@5j:-?;PX!l?9L%p?L1,foL4&EZGHLsnqT_;8ns$`]X&`l#f+Z;*q'bg5,mahEKfKCsk9C?_*.L%$C;%MKm)JZFOHJ:9I+@0Cq!=L]f.CofJ8KMAk?<40#\OPPFW9"=T;ZPJ\[kiR:CaB%)kgGF]-_e.3>>cPa$I3=h$-fK'Z3K)]Qp'6)E)qHc*KnHT1.M\L2WV]#Cb_h)P*'1jDBRV53A,R)m";E%HcOReP6F_,(,G,:/*ZZA!gnsrhJG?1k[$'0tJ5`#7)j,Xd,oLo"cL@VXAJ&j>#D(Nbet_+PL&Q&&6$QlB^sK8AM$9#T<1A*us8TC090oh'C_WChja)$nP]@7QB^D?E%IAD9S"82aXoN)5fqfDeue(_"ML8X>K0T#epgW877BoL(]^"kW@VcE;&Sf4gf=;']f9Kp'^]",XSG('XQ%'][W,m0,1A3?()4YKI/_4lI%d2^TeP7t+Vqt1R@3p3]SRqE%H0*jOp2LX]JM>/&+KElp,k$tD5@e]5iN(VML0%/W\(`X/Y_EXpALebo1n>o_kPmA,_aW39h8V7pq"p>bhmATe`r(d3Y)db>0+H*N2W`g%:GL^hoBV.6WWRrRWEhu[[Z7Es&QL]n$4A5FqW$oSdOE+m%u!doQH`Uh:bg_k)J8r`iR(7Y^<7WoR0Jj%jlgqu\3Cho85nEbr+Y!h/9m;ouFhlXScu8VPnRo@BBFf%+?J_iYm2[rf-"XVS2$FKFq4KN-[!t/eT6e@s,rW-puS\WE0N6@PA-OHD$m)1k;2+,>QQJj4#s]N2K"p3VjN>MV2drG-@u#Sae$]Cs..2h07_?W#59b_6_3HPW>,Pk.5@cEc5P";oMK^aDk[J>Fi;I4^TB>l6rD%RH]h(N+[%)^p/f'i2"=*[@2*4pO8k+ohVln]tZ("FUbb3">q=$@%VN!rpX-VadE?of>RS:Ed.5&hbH!7UHTi=PWAE8fpa!)1FCKL=,L^kJ7"!&,FS&Iq+!!uGj(!5N^4a,!4mHg(/`Xc@IAo)etBi6O3LT_iZBZoX5abmsfAN^(j/!m1HGKg*O;\G6.

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