Ejercicio 293

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CAPITULO XXXVII

Progresiones Geométricas
Ejercicio 293
Hallar la suma de los:
  1. 5 primeros términos de ÷ ÷ 6:3:1 1 2 …….
    Sea: a=6,r= 3 = 1 2 ,n=5 u =a r n1 u =6 ( 1 2 ) 51 u = 2 .3( 1 2 ) u = 3 8 S = ura r1 S = 3 8 ( 1 2 ) 6 1 2 1 S = 3 16 6 1 2 S = 396 1 2 S = 93 8 11 5 8
  2. 6 primeros términos de ÷ ÷ 4:8:16…….
    Sea: a=4,r= 4 =2,n=6 u =a r n1 u =4 (2 ) 61 u = 2 2 . (2 ) 5 = 2 7 u =128 S = ura r1 S = 128(2 ) 4 21 S = 2564 3 S = 3 S =84
  3. 7 primeros términos de ÷ ÷ 12:4:1 1 3 …….
    Sea: a=12,r= 4 = 1 3 ,n=7 u =a r n1 u =12 ( 1 3 ) 71 u = 3 .4( 1 3 ) u = 4 3 5 S = ura r1 S = 4 3 5 ( 1 3 ) 12 1 3 1 S = 4 3 6 12 2 3 S = 412. 3 6 3 2 3 S = 2 (22. 3 7 ) 2 . 3 5 S = 4372 243 17 241 243
  4. 10 primeros términos de ÷ ÷ 1 4 : 1 2 :1…….
    Sea: a= 1 4 ,r= 1 2 1 =2,n=10 u =a r n1 u = 1 4 ( 2 ) 101 u = 1 2 2 . 2 = 2 7 u =128 S = ura r1 S = 128( 2 ) 1 4 21 S =256 1 4 S = 1023 4 255 3 4
  5. 8 primeros términos de ÷ ÷ 2 1 4 :1 1 2 …….
    Sea: a= 9 4 ,r= 3 2 = 2 3 ,n=8 u =a r n1 u = 9 4 ( 2 3 ) 81 u = 3 2 2 2 . 2 3 u = 2 5 3 5 S = ura r1 S = 2 5 3 5 ( 2 3 ) 9 4 2 3 1 S = 2 6 3 6 3 2 2 2 1 3 S = 2 8 3 8 3 6 . 2 2 (3 ) S = 6305 972 6 473 972
  6. 7 primeros términos de ÷ ÷ 1 10 : 1 5 : 2 5 …….
    Sea: a= 1 10 ,r= 1 5 1 =2,n=7 u =a r n1 u = 1 10 (2 ) 71 u = 1 10 . (2 ) 6 u = u = 32 5 S = ura r1 S = 32 5 (2 ) ( 1 10 ) 21 S = 64 5 + 1 10 3 S = 128+1 10 3 S = 10 3 S = 43 10 4 3 10
  7. 10 primeros términos de ÷ ÷ 6:3:1 1 2 …….
    Sea: a=6,r= 3 = 1 2 ,n=10 u =a r n1 u =6 ( 1 2 ) 101 u = 2 .3( 1 2 ) u = 3 2 8 S = ura r1 S = 3 2 8 ( 1 2 ) (6 ) 1 2 1 S = 3 2 9 +6 1 2 S = 3+3. 2 10 2 1 2 S = 3(1+ 2 10 ) 2 8 S = 3069 256 11 253 256
  8. 8 primeros términos de ÷ ÷ 2:1: 1 2 …….
    Sea: a=2,r= 1 2 ,n=8 u =a r n1 u =2 ( 1 2 ) 81 u = 2 ( 1 2 ) u = 1 2 6 u = 1 64 S = ura r1 S = 1 64 ( 1 2 ) 2 1 2 1 S = 1 128 2 3 2 S = 3 2 S = 85 64 1 21 64
  9. 6 primeros términos de ÷ ÷ 3 2 :1: 2 3 …….
    Sea: a= 3 2 ,r= 1 3 2 = 2 3 ,n=6 u =a r n1 u = 3 2 ( 2 3 ) 61 u = 3 2 . 2 3 u = 2 4 3 4 u = 16 81 S = ura r1 S = 2 4 3 4 ( 2 3 ) 3 2 2 3 1 S = 2 5 3 5 3 2 1 3 S = 2 6 3 6 2. 3 5 1 3 S = 2 6 3 6 2. 3 4 S = 665 162 4 17 162
  10. 6 primeros términos de ÷ ÷ 9:3:1…….
    Sea: a=9,r= 3 = 1 3 ,n=6 u =a r n1 u =9 ( 1 3 ) 61 u = 3 2 ( 1 3 ) u = 1 3 3 u = 1 27 S = ura r1 S = 1 3 3 ( 1 3 ) 9 1 3 1 S = 1 3 4 3 2 4 3 S = 1 3 6 3 4 3 S = 1 3 6 4. 3 3 S = S = 182 27 6 20 27