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MathMagic Equation - www.mathmagic.com QCM Suites n u m é r i q u e s Q u e s t i o n 1 : la suite de terme g é n é r a l u n n N * = cos 1 n n 2 tend vers : + e 1 2 e e 1 2 n ' a d m e t pas de limite Q u e s t i o n 2 : Soit la suite u n n N * = 1 + 1 2 + 1 3 + ... + 1 n la suite u n est convergente la suite u n est positive la suite u n est m a j o r é e la suite u n est croissante Q u e s t i o n 3 : La somme S = n = 1 + n 5 n vaut : 1 4 4 5 5 16 1 16 Q u e s t i o n 4 : Soit la suite de terme g é n é r a l a n = a 2 n 1 + a 2 n + 1 2 , n 1 la suite a n est constante ou divergente la suite a n est arithmetique la suite a n est g é o m e t r i q u e On peut pas en conclure Q u e s t i o n 5 : La suite x n n N definit par x n = π n π 10 est : b o r n é e croissante convergente d é c r o i s s a n t e Q u e s t i o n 6 On note S n = v 0 + v 1 + ... + v n pour tout n N avec v n = ln n + 2 n + 3 Alors : lim n + S n = 0 lim n + S n = 1 lim n + S n = 2 lim n + S n = 3 lim n + S n = Q u e s t i o n 7 Soit la suite α n d é f i n i e par α n = n n + a n + b avec a , b R On a alors : lim n + α n = a b lim n + α n = a + b lim n + α n = a + b 2 lim n + α n = a + b Q u e s t i o n 8 k = 1 n 2 n k C n k vaut : 1 1 n 1 2 n 0 1 n 2 n 1 n + 2 n MMF.7h]?*`00kA[KL]|fmP_l3gYKJHOA402_WNV3k6ZmW[FU[:BV)k?Z0f)c;]NBj5:BVfc67nbo:002h249*9OHTlB][cPGh5aaL41ZOS7jagQb=IQMS4LWWdkVIi?QH3JNM:nBcJmGbFefgGUKi9fO|UGW8NZk_I?ik69f)Na^O|oYn=e`(ZGc^[kC2I`)Xoh`V0fkM8`X2[_|[a]mAgl88`koloIbL37ZmThNCnKChFaf(CYW(ZOCdN1Zf?eaWAJMJK[II:]Kb[gNM5gWjVZFO]RLi_WMJBV0HQ75WZF[cKKh)4YoEfSL*)(BCB[dN75cGZCYWJ9i)YYHcVl|QdYdh31U)X?E9_]]VbS^d9UUbgCMXJbMBKi(EXXB)FOi]|RXJE3If(R?G;eib60f(]R=K8HSVnG8H3X:31ZHSDMjji7IO=`dG`S7YZPKc(Lflk7=O6``7a_(afKc|MilK3JO6:9?3)JCY_TLognjLk0CUD?T8(LGJ4c7a2o7Q8iA80PN1B8amQT12jj00Z4HQf2U2(j)`FbJ_lPYImmgfMP]Qd`=9(HH|30eo7iD0T`=90RnTWc?]I3hT9[VmXV08PiQ(Cl6*[PR_P**d0CC)DR(VGR?28293o]RIL*DT)(0;|clP8R4V2L22L*eiK0;S*HZH)J1F084F8NQ2k0?YT0EL5SYQZ)jC)P30QDP23R4l1Q8P:P0D|23dO5[Ri)PTT]2H3R9h=Xa03bXP|MDR(*27PJVNPBbNA0XEO0T8e?QSB::K93i4`53_1PHh[|`]J0J?U=3c?MQ:7b?iHU(1im_2fVE7l0Ll9TFF8`S(8j[C0]L(0JY4)3:Y*5d*|35Bl2_EPd2|18;0Y5j116gF49a9BF4Vb64RA02nB6C;cI3j77?QP;bhAAV_9*IPU*(VGa?S7TN2YDS9Yj8]B8X?R[cD484TV0RAVDFB2RXC8^H0VmD?HP09JiDRed`1^j?(I0HTlZc|*OB)oI1H)80CPU1a|*A16:``i3[eVZ;RnXP[QD^0RZ?jd70[`:4g5YAL|(J545g8ALT8T9^SEH[SHPG9TDRg;F:F6i;1OY`HP21d?4ZP3WUSEZbiQEN85Gd4BnAF08H0WaWB02jQ=M8[20H6lC;I:*PT1X8Plf123bWN9UD1*HA|3l*;IA^aLScDfXX:ZF_F6_AhLEB)I9Gb`YB;STO_:E7Y^]`]Ae2oiM*:I=A4HOZE?X]Z3b;)1gnAh9:j:a8h2?a=n:ESe4m^R8A56hUQhVPnQcCnQKDP6]QdRYDe91C`aXe||j=kMkHhBc4*Z;ENS8NckY^WnhW]ao*Gl*6=(TXRYl;benjmDj|a24=3[MkbI90=(bJa[(T|:IcD1Bih6)miVVfBXZ?9AaBN9CN9Y^dQ2(:Cm95||WbEHV9:NIMDVC9ndF:QKK(Q)7VFT1(nN67CI4868(I0h4S07LZL1k0W*VL3g0o25bPLeRX*dHV;j1Hif3Ga(h_1L1[o380gLI_0M1__?)_)`kkKLoaGUmi3XMecn6XkCTL]cg7VoV6igPSgo1LXhTGB5gj46?n45o77QSI`k[WB=C`78TKW_?LU^Lle?JLQj7W?5;gW)Ne?NOiKLmi*M]cG]S`G;:P^hJe[SA18_i3F*A0abhOLhR`(YHD=GJ?XGTmH0Q?L7Y|4LYlMSVQ1F2D5l]TdF6?84A=;;mAgnEEUG6aHfEbO_[VM;5=AMUeWL3gRMmRS9gc8_Wh_ElFF8;386`^);hL=`GCT|Bo=0?4WlRDTfYjJ5UeLbZEJ8LMAbh=Ng]*CSWm5gL:7Deo_)ZbL5n(IUfVmOBOhim)1m(Q8cjb]DNchFS6W^aL|N)|mfUnnVUnmUo7XMGILEaJ4abVkLoMOimMmNICN[[d])CY=]^TJa_7J[]l:[;O]YC[|BH4XCiADRRI9Bgj[|V4niSnnkVkB5Y256g=U32CKbbdCEX|;NCKYmECTB`T0cf?j75KnZZkIC0:P)_XEmb?biT[*7eTGo=gGM:SOcaZHF=NiHebhU*|YW11P7XJeQ6G4AXdn7^?Rfd]QZ9*I`n`?J:]8FFlc]LEHd]OaUKZfhYHBD2Dl4h:UdQ(NXlEfWE;;7=(0bGL5)[Li5D)K];3?^fS)Ad;lhf1GmfHhoj*5^fTEUBAY2g?n[4[9kEX98`dF8c3gF_=F5o*g:::(HE^UTRGNGWW|S2V0N?bQ84Ha;A6Z(EDLI(bE|nVI11k)^M7HRT*mkI3HjC=ETGG5Z6VIHZKU4Vd`i)JCObgi6JIK|`(mhTV_bAAEk0TKI4]FK7KGDYaZiC:9JIiI]5(EfPU[EIX3bZ6Ged1e6F0HMMJRUl[WGHF_l=UT)NBdCJignlOHO*a5OoP7KAg6[K9kEa|i9OVF525JVgI6]OiRQh(]kAICgMGkFo3Y?]lWFfbQeMScc;iGehlVLcA7RaO|cWGAIj]elUZ[hY?S1GodVIJ_]Ae`)Z`d1*8GT1Wk?hY3Wa=|I3=PJm]dcSIZhh6kMBEZMT`lUNZZXJUG^]Q7`(CA);[GIZBbK^dBgX=IUM0LbPOTZdUUW]dSAHoN|gHkVc9?TNJKi;V7BH=K3R;=;Yc3);lUc3);(k^Bn_VlejjgCZ|CCCLJbFiLJm](bCkE3A3GJP^0YHP]3XWBDS(1D=NjkBZfJX0_aEX`bdg|ibRV|Nb4SBlli8j=UXdZ:(a:GEG:V=8ihj^U(Ojnh^FEM]3=T_YBineNfGVTMgMN|)?FR=;_[G|a^`;mHH_iY2Tb3JodU||NgSgFVbjOLZYALF19W72N:G7gjNJDknTJ2kiYHZ6YFP:GRnfaCk=WWmL|fNj`;Lh?nb)`27?lIkW]Vn9nTgjBkJb7KCgBF4VkV6]jD5Z^hh7YQ?8eY)hY_?*N9iY9I|NcafeFOKXF=^Cg^O5bWP1|li|GWH)W;gcLVhmTFjN3[Y[]EY8^HjVBUAYU=]Zg_CX7=CLA)a[^MZe30n9MZb53UW;l|3YH(7F*n0ngeZfnbJgGM*)N`1Y?(8NdV|cMBoKmPPf_d(_EYZBKRTf1kBO[HN?Ajb1cKNZo*h*`eHK;7;MFiZ3k]|HVd:`b9J2cB1NUbJNJgb:[7ogloS2QL3mb`WV:lZObPWh;bNXLVIoC_FJW)3DFlFJW9e=SYk7NKI7F^eL33oSb;miHSL0Bh(5KP17B]hcbgAI82h0l=VHiOJUFl7*9BFm0niQcb?boMhR3ga41G|VZk;9g=UORKfk^LTaCKdUfI=GdJ2lk5i9C7]5WgIo:WliXVSH=|;;k=Y_h8alOSO_nYB7lM=bcD2XCfkD0b7AAiG?Pci)lK[R|foI|)Cm[ThWTQ66kkAE]5^1KA*XV2O7g6SEBjLkcH^X^P(ZM(n`aZ[fZU[cVR[ZnnXCU5:J`]D]DnRkNULZ3CkS4OG=0QkeQ3]K7oOIKm7iY:2FA)J6[1gTmRWDF)_HcjoFUU6ONoQbU^bO[RmQRNW9A)fHnI;AnCHMoKGiC7bHl8_jk?7TlN*?8K9F)`.mmf

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