Question

Bài 6: Cho C = 1/3 + 1/3 ² + 1/3³ + … + 1/3⁹⁹ CMR C < ½ Giúp mik với… Pls 🙏🏿

Answer 1

`1/3C = 1/3(1/3 + 1/3^2 + ... + 1/3^99)`

`= 1/3^2 + 1/3^3 + ... + 1/3^100`

`=> C - 1/3C = 1/3 + 1/3^2 + ... + 1/3^99 - 1/3^2 - 1/3^3 + ... - 1/3^100`

`=> 2/3C = 1/3  -1/3^100`

`=> C = 1/2 - 1/3^100 : 2/3 < 1/2`.