Răspuns:
f < 1
Explicație pas cu pas:
f = (2⁰+2¹+2²+............2⁴⁹) / (5⁰+5¹+5²+..........5²⁵) = a/b
a = 2⁰+2¹+2²+............2⁴⁹ I· 2 =>
2a = 2¹+2²+2³+......+2⁴⁹+2⁵⁰
2a = a-1 +2⁵⁰ => a = 2⁵⁰-1
b = 5⁰+5¹+5²+..........5²⁵ I·5 =>
5b = 5¹+5²+5³+.....+5²⁵+5²⁶
5b = b-1+5²⁶ => 4b = 5²⁶-1 =>
b = (5²⁶-1)/4
f = 4(2⁵⁰-1)/(5²⁶-1)
f < 1
2⁵⁰ = 2¹⁰ˣ⁵ = (2¹⁰)⁵ = 1024⁵
5²⁶ = 5·5⁵ˣ⁵ = 5·(5⁵)⁵ = 5·3125⁵ =>
4(2⁵⁰-1) < 5²⁶-1 => f < 1
#copaceibrainly
