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222-9+11+12:2*14+14 = ? ( )

## Toán Lớp 7: 132 + 1/3 mũ 2 + 1/3 mũ 3 + chấm chấm chấm + 1/2 mũ 2020 giúp mik vs mn

Toán Lớp 7: 132 + 1/3 mũ 2 + 1/3 mũ 3 + chấm chấm chấm + 1/2 mũ 2020
giúp mik vs mn

1. Đặt A=1/3+1/3^2+1/3^3+…+1/3^2020
⇒3A=1+1/3+1/3^2+…+1/3^2019
⇒3A-A=(1+1/3+1/3^2+…+1/2^2019)-(1/3+1/3^2+1/3^3+…+1/3^2020)
⇒2A=1-1/3^2020
⇒2A={3^2020-1}/3^2020
⇒A={3^2020-1}/3^2021

2. Giải đáp:
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Đề 1/3 + 1/3^2 + 1/3^3 + … + 1/3^{2020}
Đặt A = 1/3 + 1/3^2 + 1/3^3 + … + 1/3^{2020}
↔ 3A = 3 (1/3 + 1/3^2 + 1/3^3 + … + 1/3^{2020})
↔ 3A = 1 + 1/3 + 1/3^2 + … + 1/3^{2019}
↔ 3A – A = (1 + 1/3 + 1/3^2 + … + 1/3^{2019})- (1/3 + 1/3^2 + 1/3^3 + … + 1/3^{2020})
↔ (3-1) A= 1 – 1/3^{2020}
↔ 2A =1 – 1/3^{2020}
↔ A = (1 – 1/3^{2020})/2
Vậy A = (1 – 1/3^{2020})/2
$\\$
Đề 1/2 + 1/2^2 + 1/2^3 + … + 1/2^{2020}
Đặt A = 1/2 + 1/2^2 + 1/2^3 + … + 1/2^{2020}
↔ 2A = 2 (1/2 + 1/2^2 + 1/2^3 + … + 1/2^{2020})
↔ 2A = 1 + 1/2 + 1/2^2 + … + 1/2^{2019}
↔ 2A – A = (1 + 1/2 + 1/2^2 + … + 1/2^{2019}) – (1/2 + 1/2^2 + 1/2^3 + … + 1/2^{2020})
↔ (2-1)A = 1 – 1/2^{2020}
↔ A = 1 – 1/2^{2020}
Vậy A = 1- 1/2^{2020}