Ejercicio 296

Comparte esto 👍👍
CAPITULO XXXVII

Progresiones Geométricas
Valor de una fracción decimal periódica
Ejercicio 296
Hallar por la suma al infinito, el valor de las fracciones decimales:
  1. 0.66666…..
    0.6666… = 6 10 + 6 100 + 6 1000 +…. Donde: a= 6 10 ,r= 6 10 0 6 1 0 = 1 10 S = a 1r S = 6 10 1 1 10 S = 10 10 S = 2 3 0.6666…. = 2 3
  2. 0.1212…..
    0.1212… = 12 100 + 12 10000 + 12 1000000 +…. Donde: a= 12 100 ,r= 12 100 00 12 1 00 = 1 100 S = a 1r S = 12 100 1 1 100 S = 100 100 S = 4 33 0.121212…. = 4 33
  3. 0.159159…..
    0.159159… = 159 1000 + 159 1000000 +…. Donde: a= 159 1000 ,r= 159 1000 000 159 1 000 = 1 1000 S = a 1r S = 159 1000 1 1 1000 S = 1000 1000 S = 53 333 0.159159159…. = 53 333
  4. 0.3232……
    0.323232… = 32 100 + 32 10000 +…. Donde: a= 32 100 ,r= 32 100 00 32 1 00 = 1 100 S = a 1r S = 32 100 1 1 100 S = 32 100 99 100 S = 32 99 0.323232…. = 32 99
  5. 0.144144…….
    0.144144… = 144 1000 + 144 1000000 +…. Donde: a= 144 1000 ,r= 144 1000 000 144 1 000 = 1 1000 S = a 1r S = 144 1000 1 1 1000 S = 1000 1000 S = 48 333 0.144144144…. = 48 333
  6. 0.3555……
    0.35555… = 3 10 + 5 100 + 5 1000 + 5 10000 …. Donde: a= 5 100 ,r= 5 10 00 5 1 00 = 1 10 S = a 1r S = 5 100 1 1 10 S = 5 10 0 9 10 S = 5 90 0.35555…. = 3 10 + 5 90 = 27+5 90 0.35555…. = 32 90
  7. 0.18111….
    0.18111… = 18 100 + 1 1000 + 1 10000 +…. Donde: a= 1 1000 ,r= 1 10 000 1 1 000 = 1 10 S = a 1r S = 1 1000 1 1 10 S = 1 100 0 9 10 S = 1 900 0.1811111…. = 18 100 + 1 900 = 162+1 900 0.1811111…. = 163 900
  8. 0.31818….
    0.3181818… = 3 10 + 18 1000 + 18 100000 +…. Donde: a= 18 1000 ,r= 18 100 000 18 1 000 = 1 100 S = a 1r S = 18 1000 1 1 100 S = 10 00 100 S = 2 110 = 1 55 0.3181818…. = 3 10 + 1 55 = 33+2 110 = 0.3181818…. = 7 22
  9. 2.1818……
    2.181818… =2+ 18 100 + 18 10000 +…. Donde: a= 18 100 ,r= 18 100 00 18 1 00 = 1 100 S = a 1r S = 18 100 1 1 100 S = 100 100 S = 2 11 2.181818…. =2+ 2 11 = 22+2 11 2.181818…. = 24 11