Toán Tính tổng các phân số sau: 1/3+1/3^2+1/3^3+………+1/3^2020 11/09/2021 By Ruby Tính tổng các phân số sau: 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) = 1+1/3+1/3^2+1/3^3+………+1/3^2019 => 3A- A= 1+1/3+1/3^2+1/3^3+………+1/3^2019- 1/3-1/3^2-1/3^3-………-1/3^2020 => 2A= 1- 1/3^2020= (3^2020- 1)/ 3^2020 => A= (3^2020- 1)/ 2. 3^2020 Trả lời
Đặt A = $\frac{1}{3}$ + $\frac{1}{3^{2}}$ + $\frac{1}{3^{3}}$+ …+$\frac{1}{3^{2020}}$ ⇒ 3A =1+ $\frac{1}{3}$ + $\frac{1}{3^{2}}$ + $\frac{1}{3^{3}}$+ …+$\frac{1}{3^{2019}}$ ⇒ 3A- A = (1+ $\frac{1}{3}$ + $\frac{1}{3^{2}}$ + $\frac{1}{3^{3}}$+ …+$\frac{1}{3^{2019}}$)-($\frac{1}{3}$ + $\frac{1}{3^{2}}$ + $\frac{1}{3^{3}}$+ …+$\frac{1}{3^{2020}}$ ) ⇒ 2A = 1- $\frac{1}{3^{2020}}$ ⇒ A = $\frac{1- \frac{1}{3^{2020}}}{2}$ Trả lời
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)
= 1+1/3+1/3^2+1/3^3+………+1/3^2019
=> 3A- A= 1+1/3+1/3^2+1/3^3+………+1/3^2019- 1/3-1/3^2-1/3^3-………-1/3^2020
=> 2A= 1- 1/3^2020= (3^2020- 1)/ 3^2020
=> A= (3^2020- 1)/ 2. 3^2020
Đặt A = $\frac{1}{3}$ + $\frac{1}{3^{2}}$ + $\frac{1}{3^{3}}$+ …+$\frac{1}{3^{2020}}$
⇒ 3A =1+ $\frac{1}{3}$ + $\frac{1}{3^{2}}$ + $\frac{1}{3^{3}}$+ …+$\frac{1}{3^{2019}}$
⇒ 3A- A = (1+ $\frac{1}{3}$ + $\frac{1}{3^{2}}$ + $\frac{1}{3^{3}}$+ …+$\frac{1}{3^{2019}}$)-($\frac{1}{3}$ + $\frac{1}{3^{2}}$ + $\frac{1}{3^{3}}$+ …+$\frac{1}{3^{2020}}$ )
⇒ 2A = 1- $\frac{1}{3^{2020}}$
⇒ A = $\frac{1- \frac{1}{3^{2020}}}{2}$