nhớ tích nha Nguyễn Bảo Châu

123+123=246

741-41=700

Phần B nek :

 Gọi tử là : T

\(\Rightarrow T=1+3+3^2+.....+3^9\)

\(\Rightarrow3T=3+3^2+3^3+.....+3^{10}\)

\(\Rightarrow3T-T=3^{10}-1\)

\(\Rightarrow T=\frac{3^{10}-1}{2}\)

Gọi mẫu là : H

\(\Rightarrow H=1+3+3^2+.....+3^8\)

\(\Rightarrow3H=3+3^2+3^3+.....+3^9\)

\(\Rightarrow3H-H=3^9-1\)

\(\Rightarrow H=\frac{3^9-1}{2}\)

\(\Rightarrow B=\frac{T}{H}=\frac{\frac{3^{10}-1}{2}}{\frac{3^9-1}{2}}=\frac{29524}{9841}=3,0001.....\)

Cho a sửa câu a nha :

 \(\Rightarrow A=\frac{R}{M}=\frac{\frac{5^{10}-1}{4}}{\frac{5^9-1}{4}}=\frac{2441406}{488281}=5,000002048\)

Vậy \(\Rightarrow A>B\left(đpcm\right)\)