Ejercicio 293

Ejercicio 293

1. 5 primeros términos de ÷ ÷ 6:3:1 1 2 …….
   Sea: a=6,r= 3 = 1 2 ,n=5 u =a r n–1 u =6 ( 1 2 ) 5–1 u = 2 .3( 1 2 ) u = 3 8 S = ur–a r–1 S = 3 8 ( 1 2 ) –6 1 2 –1 S = 3 16 –6 – 1 2 S = 3–96 – 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 n–1 u =4 ( –2 ) 6–1 u = 2 2 . ( –2 ) 5 =– 2 7 u =–128 S = ur–a r–1 S = –128( –2 ) –4 –2–1 S = 256–4 –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 n–1 u =12 ( 1 3 ) 7–1 u = 3 .4( 1 3 ) u = 4 3 5 S = ur–a r–1 S = 4 3 5 ( 1 3 ) –12 1 3 –1 S = 4 3 6 –12 – 2 3 S = 4–12. 3 6 3 – 2 3 S =– 2 ( 2–2. 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 n–1 u = 1 4 ( 2 ) 10–1 u = 1 2 2 . 2 = 2 7 u =128 S = ur–a r–1 S = 128( 2 ) – 1 4 2–1 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 n–1 u = 9 4 ( 2 3 ) 8–1 u = 3 2 2 2 . 2 3 u = 2 5 3 5 S = ur–a r–1 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 n–1 u =– 1 10 ( –2 ) 7–1 u =– 1 10 . ( –2 ) 6 u =– u =– 32 5 S = ur–a r–1 S = – 32 5 ( –2 ) –( – 1 10 ) –2–1 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 n–1 u =–6 ( 1 2 ) 10–1 u =– 2 .3( 1 2 ) u =– 3 2 8 S = ur–a r–1 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 n–1 u =2 ( – 1 2 ) 8–1 u = 2 ( – 1 2 ) u =– 1 2 6 u =– 1 64 S = ur–a r–1 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 n–1 u = 3 2 ( 2 3 ) 6–1 u = 3 2 . 2 3 u = 2 4 3 4 u = 16 81 S = ur–a r–1 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 n–1 u =9 ( – 1 3 ) 6–1 u = 3 2 ( – 1 3 ) u =– 1 3 3 u =– 1 27 S = ur–a r–1 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