Triangulo de Pascal

87
Univer ENP.

description

ejemplo del triangulo de pascal

Transcript of Triangulo de Pascal

Hoja1

111(x+y)121(x2+y2)1331(x3+y3)14641(x4+y4)15101051(x5+y5)1615201561(x6+y6)172135352171(x7+y7)18285670562881(x8+y8)193684126126843691(x9+y9)1104512021025221012045101(x10+y10)1115516533046246233016555111(x11+y11)1126622049579292479249522066121(x12+y12)113782867151,2871,7161,7161,28771528678131(x13+y13)114913641,0012,0023,0033,4323,0032,0021,00136491141(x14+y14)1151054551,3653,0035,0056,4356,4355,0053,0031,365455105151(x15+y15)1161205601,8204,3688,00811,44012,87011,4408,0084,3681,820560120161(x16+y16)1171366802,3806,18812,37619,44824,31024,31019,44812,3766,1882,380680136171(x17+y17)1181538163,0608,56818,56431,82443,75848,62043,75831,82418,5648,5683,060816153181(x18+y18)1191719693,87611,62827,13250,38875,58292,37892,37875,58250,38827,13211,6283,876969171191(x19+y19)1201901,1404,84515,50438,76077,520125,970167,960184,756167,960125,97077,52038,76015,5044,8451,140190201(x20+y20)1212101,3305,98520,34954,264116,280203,490293,930352,716352,716293,930203,490116,28054,26420,3495,9851,330210211(x21+y21)1222311,5407,31526,33474,613170,544319,770497,420646,646705,432646,646497,420319,770170,54474,61326,3347,3151,540231221(x22+y22)1232531,7718,85533,649100,947245,157490,314817,1901,144,0661,352,0781,352,0781,144,066817,190490,314245,157100,94733,6498,8551,771253231(x23+y23)1242762,02410,62642,504134,596346,104735,4711,307,5041,961,2562,496,1442,704,1562,496,1441,961,2561,307,504735,471346,104134,59642,50410,6262,024276241(x24+y24)1253002,30012,65053,130177,100480,7001,081,5752,042,9753,268,7604,457,4005,200,3005,200,3004,457,4003,268,7602,042,9751,081,575480,700177,10053,13012,6502,300300251(x25+y25)1263252,60014,95065,780230,230657,8001,562,2753,124,5505,311,7357,726,1609,657,70010,400,6009,657,7007,726,1605,311,7353,124,5501,562,275657,800230,23065,78014,9502,600325261(x26+y26)1273512,92517,55080,730296,010888,0302,220,0754,686,8258,436,28513,037,89517,383,86020,058,30020,058,30017,383,86013,037,8958,436,2854,686,8252,220,075888,030296,01080,73017,5502,925351271(x27+y27)1283783,27620,47598,280376,7401,184,0403,108,1056,906,90013,123,11021,474,18030,421,75537,442,16040,116,60037,442,16030,421,75521,474,18013,123,1106,906,9003,108,1051,184,040376,74098,28020,4753,276378281(x28+y28)1294063,65423,751118,755475,0201,560,7804,292,14510,015,00520,030,01034,597,29051,895,93567,863,91577,558,76077,558,76067,863,91551,895,93534,597,29020,030,01010,015,0054,292,1451,560,780475,020118,75523,7513,654406291(x29+y29)1304354,06027,405142,506593,7752,035,8005,852,92514,307,15030,045,01554,627,30086,493,225119,759,850145,422,675155,117,520145,422,675119,759,85086,493,22554,627,30030,045,01514,307,1505,852,9252,035,800593,775142,50627,4054,060435301(x30+y30)1314654,49531,465169,911736,2812,629,5757,888,72520,160,07544,352,16584,672,315141,120,525206,253,075265,182,525300,540,195300,540,195265,182,525206,253,075141,120,52584,672,31544,352,16520,160,0757,888,7252,629,575736,281169,91131,4654,495465311(x31+y31)1324964,96035,960201,376906,1923,365,85610,518,30028,048,80064,512,240129,024,480225,792,840347,373,600471,435,600565,722,720601,080,390565,722,720471,435,600347,373,600225,792,840129,024,48064,512,24028,048,80010,518,3003,365,856906,192201,37635,9604,960496321(x32+y32)1335285,45640,920237,3361,107,5684,272,04813,884,15638,567,10092,561,040193,536,720354,817,320573,166,440818,809,2001,037,158,3201,166,803,1101,166,803,1101,037,158,320818,809,200573,166,440354,817,320193,536,72092,561,04038,567,10013,884,1564,272,0481,107,568237,33640,9205,456528331(x33+y33)1345615,98446,376278,2561,344,9045,379,61618,156,20452,451,256131,128,140286,097,760548,354,040927,983,7601,391,975,6401,855,967,5202,203,961,4302,333,606,2202,203,961,4301,855,967,5201,391,975,640927,983,760548,354,040286,097,760131,128,14052,451,25618,156,2045,379,6161,344,904278,25646,3765,984561341(x34+y34)1355956,54552,360324,6321,623,1606,724,52023,535,82070,607,460183,579,396417,225,900834,451,8001,476,337,8002,319,959,4003,247,943,1604,059,928,9504,537,567,6504,537,567,6504,059,928,9503,247,943,1602,319,959,4001,476,337,800834,451,800417,225,900183,579,39670,607,46023,535,8206,724,5201,623,160324,63252,3606,545595351(x35+y35)1366307,14058,905376,9921,947,7928,347,68030,260,34094,143,280254,186,856600,805,2961,251,677,7002,310,789,6003,796,297,2005,567,902,5607,307,872,1108,597,496,6009,075,135,3008,597,496,6007,307,872,1105,567,902,5603,796,297,2002,310,789,6001,251,677,700600,805,296254,186,85694,143,28030,260,3408,347,6801,947,792376,99258,9057,140630361(x36+y36)1376667,77066,045435,8972,324,78410,295,47238,608,020124,403,620348,330,136854,992,1521,852,482,9963,562,467,3006,107,086,8009,364,199,76012,875,774,67015,905,368,71017,672,631,90017,672,631,90015,905,368,71012,875,774,6709,364,199,7606,107,086,8003,562,467,3001,852,482,996854,992,152348,330,136124,403,62038,608,02010,295,4722,324,784435,89766,0457,770666371(x37+y37)1387038,43673,815501,9422,760,68112,620,25648,903,492163,011,640472,733,7561,203,322,2882,707,475,1485,414,950,2969,669,554,10015,471,286,56022,239,974,43028,781,143,38033,578,000,61035,345,263,80033,578,000,61028,781,143,38022,239,974,43015,471,286,5609,669,554,1005,414,950,2962,707,475,1481,203,322,288472,733,756163,011,64048,903,49212,620,2562,760,681501,94273,8158,436703381(x38+y38)1397419,13982,251575,7573,262,62315,380,93761,523,748211,915,132635,745,3961,676,056,0443,910,797,4368,122,425,44415,084,504,39625,140,840,66037,711,260,99051,021,117,81062,359,143,99068,923,264,41068,923,264,41062,359,143,99051,021,117,81037,711,260,99025,140,840,66015,084,504,3968,122,425,4443,910,797,4361,676,056,044635,745,396211,915,13261,523,74815,380,9373,262,623575,75782,2519,139741391(x39+y39)1407809,88091,390658,0083,838,38018,643,56076,904,685273,438,880847,660,5282,311,801,4405,586,853,48012,033,222,88023,206,929,84040,225,345,05662,852,101,65088,732,378,800113,380,261,800131,282,408,400137,846,528,820131,282,408,400113,380,261,80088,732,378,80062,852,101,65040,225,345,05623,206,929,84012,033,222,8805,586,853,4802,311,801,440847,660,528273,438,88076,904,68518,643,5603,838,380658,00891,3909,880780401(x40+y40)14182010,660101,270749,3984,496,38822,481,94095,548,245350,343,5651,121,099,4083,159,461,9687,898,654,92017,620,076,36035,240,152,72063,432,274,896103,077,446,706151,584,480,450202,112,640,600244,662,670,200269,128,937,220269,128,937,220244,662,670,200202,112,640,600151,584,480,450103,077,446,70663,432,274,89635,240,152,72017,620,076,3607,898,654,9203,159,461,9681,121,099,408350,343,56595,548,24522,481,9404,496,388749,398101,27010,660820411(x41+y41)14286111,480111,930850,6685,245,78626,978,328118,030,185445,891,8101,471,442,9734,280,561,37611,058,116,88825,518,731,28052,860,229,08098,672,427,616166,509,721,602254,661,927,156353,697,121,050446,775,310,800513,791,607,420538,257,874,440513,791,607,420446,775,310,800353,697,121,050254,661,927,156166,509,721,60298,672,427,61652,860,229,08025,518,731,28011,058,116,8884,280,561,3761,471,442,973445,891,810118,030,18526,978,3285,245,786850,668111,93011,480861421(x42+y42)14390312,341123,410962,5986,096,45432,224,114145,008,513563,921,9951,917,334,7835,752,004,34915,338,678,26436,576,848,16878,378,960,360151,532,656,696265,182,149,218421,171,648,758608,359,048,206800,472,431,850960,566,918,2201,052,049,481,8601,052,049,481,860960,566,918,220800,472,431,850608,359,048,206421,171,648,758265,182,149,218151,532,656,69678,378,960,36036,576,848,16815,338,678,2645,752,004,3491,917,334,783563,921,995145,008,51332,224,1146,096,454962,598123,41012,341903431(x43+y43)14494613,244135,7511,086,0087,059,05238,320,568177,232,627708,930,5082,481,256,7787,669,339,13221,090,682,61351,915,526,432114,955,808,528229,911,617,056416,714,805,914686,353,797,9761,029,530,696,9641,408,831,480,0561,761,039,350,0702,012,616,400,0802,104,098,963,7202,012,616,400,0801,761,039,350,0701,408,831,480,0561,029,530,696,964686,353,797,976416,714,805,914229,911,617,056114,955,808,52851,915,526,43221,090,682,6137,669,339,1322,481,256,778708,930,508177,232,62738,320,5687,059,0521,086,008135,75113,244946441(x44+y44)14599014,190148,9951,221,7598,145,06045,379,620215,553,195886,163,1353,190,187,28610,150,595,91028,760,021,74573,006,209,045166,871,334,960344,867,425,584646,626,422,9701,103,068,603,8901,715,884,494,9402,438,362,177,0203,169,870,830,1263,773,655,750,1504,116,715,363,8004,116,715,363,8003,773,655,750,1503,169,870,830,1262,438,362,177,0201,715,884,494,9401,103,068,603,890646,626,422,970344,867,425,584166,871,334,96073,006,209,04528,760,021,74510,150,595,9103,190,187,286886,163,135215,553,19545,379,6208,145,0601,221,759148,99514,190990451(x45+y45)1461,03515,180163,1851,370,7549,366,81953,524,680260,932,8151,101,716,3304,076,350,42113,340,783,19638,910,617,655101,766,230,790239,877,544,005511,738,760,544991,493,848,5541,749,695,026,8602,818,953,098,8304,154,246,671,9605,608,233,007,1466,943,526,580,2767,890,371,113,9508,233,430,727,6007,890,371,113,9506,943,526,580,2765,608,233,007,1464,154,246,671,9602,818,953,098,8301,749,695,026,860991,493,848,554511,738,760,544239,877,544,005101,766,230,79038,910,617,65513,340,783,1964,076,350,4211,101,716,330260,932,81553,524,6809,366,8191,370,754163,18515,1801,035461(x46+y46)1471,08116,215178,3651,533,93910,737,57362,891,499314,457,4951,362,649,1455,178,066,75117,417,133,61752,251,400,851140,676,848,445341,643,774,795751,616,304,5491,503,232,609,0982,741,188,875,4144,568,648,125,6906,973,199,770,7909,762,479,679,10612,551,759,587,42214,833,897,694,22616,123,801,841,55016,123,801,841,55014,833,897,694,22612,551,759,587,4229,762,479,679,1066,973,199,770,7904,568,648,125,6902,741,188,875,4141,503,232,609,098751,616,304,549341,643,774,795140,676,848,44552,251,400,85117,417,133,6175,178,066,7511,362,649,145314,457,49562,891,49910,737,5731,533,939178,36516,2151,081471(x47+y47)1481,12817,296194,5801,712,30412,271,51273,629,072377,348,9941,677,106,6406,540,715,89622,595,200,36869,668,534,468192,928,249,296482,320,623,2401,093,260,079,3442,254,848,913,6474,244,421,484,5127,309,837,001,10411,541,847,896,48016,735,679,449,89622,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7,280,033,224,900,00023,720,460,024,918,600,00016,777,886,359,088,800,00011,185,257,572,725,900,0007,023,301,266,595,310,0004,150,132,566,624,500,0002,305,629,203,680,280,0001,202,936,975,833,190,000588,671,286,046,029,000269,807,672,771,096,000115,631,859,759,041,00046,252,743,903,616,50017,231,414,395,465,0005,964,720,367,660,9601,913,212,193,400,680566,877,686,933,536154,603,005,527,32838,650,751,381,8328,815,083,648,4881,823,810,410,032340,032,449,32856,672,074,8888,361,453,6721,078,897,248119,877,47211,238,513864,50152,3942,346691(x69+y69)1702,41554,740916,89512,103,014131,115,9851,198,774,7209,440,350,92065,033,528,560396,704,524,2162,163,842,859,36010,638,894,058,52047,465,835,030,320193,253,756,909,160721,480,692,460,8642,480,089,880,334,2207,877,932,561,061,64023,196,134,763,125,90063,484,158,299,081,500161,884,603,662,658,000385,439,532,530,138,000858,478,958,817,125,0001,791,608,261,879,220,0003,508,566,179,513,470,0006,455,761,770,304,780,00011,173,433,833,219,800,00018,208,558,839,321,200,00027,963,143,931,814,700,00040,498,346,384,007,400,00055,347,740,058,143,500,00071,416,438,784,701,300,00087,038,784,768,854,700,000100,226,479,430,802,400,000109,069,992,321,755,550,000112,186,277,816,662,850,000109,069,992,321,755,550,000100,226,479,430,802,400,00087,038,784,768,854,700,00071,416,438,784,701,300,00055,347,740,058,143,500,00040,498,346,384,007,400,00027,963,143,931,814,700,00018,208,558,839,321,200,00011,173,433,833,219,800,0006,455,761,770,304,780,0003,508,566,179,513,470,0001,791,608,261,879,220,000858,478,958,817,125,000385,439,532,530,138,000161,884,603,662,658,00063,484,158,299,081,50023,196,134,763,125,9007,877,932,561,061,6402,480,089,880,334,220721,480,692,460,864193,253,756,909,16047,465,835,030,32010,638,894,058,5202,163,842,859,360396,704,524,21665,033,528,5609,440,350,9201,198,774,720131,115,98512,103,014916,89554,7402,415701(x70+y70)

Universidad Autonoma de MexicoENP. 2 Erasmo Catellanos Quinto

Nombre: Carolina Felix HernandezNo. de Cuenta: 313261956Grupo: 414Materia: Matematicas IVMaestro: Armando MoralesCiclo Escolar: 2012-2013(x29+y29) = x29 + 29x28y + 406x27y2 + 3654x26y3 + 23751x25y4 + 118755x24y5 + 475020x23y6 + 1560780x22y7 + 4292145x21y8 + 10015005x20y9 + 20030010x19y10 + 34597290x18y11 + 51895935x17y12 + 67863915x16y13 + 77558760x15y14 + 77558760x14y15 + 67863915x13y16 + 51895935x12y17 + 34597290x11y18 + 2003010x10y19 + 10015005x9y20 + 4292145x8y21 + 1560780x7y22 + 475020x6y23 + 118755x5y24 + 23751x4y25 + 3654x3y26 + 406x2y27 + 29xy28 + y29