3M=1+1/3+1/9+...+1/2187

2M=3M-M

2M=1-1/6561

2M=6560/6561

M=3280/6561

Cho \(A=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+...+\frac{1}{6561}\)

    \(\frac{1}{3}A=\frac{1}{3}\times\left(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+...+\frac{1}{6561}\right)\)

    \(\frac{1}{3}A=\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+...+\frac{1}{19683}\)

 \(A-\frac{1}{3}A=\left(\frac{1}{3}+\frac{1}{9}+...+\frac{1}{6561}\right)-\left(\frac{1}{9}+\frac{1}{27}+...+\frac{1}{19683}\right)\)

\(\frac{2}{3}A=\frac{1}{3}-\frac{1}{19683}\)

\(A=\frac{4840}{9683}:\frac{2}{3}=\frac{7260}{9683}\)

ta có :

= ( 1 + 59049 ) + ( 3 + 2187 ) + ( 9 + 6561 ) + ( 27 + 243 ) + ( 81 + 729 )

= 59050 + 2190 + 6570 + 270 + 810

= 59050 + ( 2190 + 810 ) + 6570 + 270

= 59050 + 3000 + 6570 + 270

= 59050 + ( 3000 + 6570 ) + 270

= 59050 + 9570 + 270

= 68620 + 270

= 68890

68890

Kết quả là 68890

Nhớ trả lời cho mình

\(A=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+...+\frac{1}{6561}\)

\(\Rightarrow A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+...+\frac{1}{3^8}\)

\(\Rightarrow3A=3.\left(\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^8}\right)\) \(=1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^7}\)

\(\Rightarrow3A-A=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}-\frac{1}{3}-\frac{1}{3^2}-\frac{1}{3^3}-...-\frac{1}{3^8}\)

\(\Rightarrow2A=1-\frac{1}{3^8}\) \(\Rightarrow A=\frac{1-\frac{1}{3^8}}{2}\)

k cho mik đi mn!Nguyễn Như Quỳnh!

\(3A=1+\dfrac{1}{3}+\dfrac{1}{9}+...+\dfrac{1}{2187}\)

\(3A-A=\left(1+\dfrac{1}{3}+\dfrac{1}{9}+...+\dfrac{1}{2187}\right)-\left(\dfrac{1}{3}+\dfrac{1}{9}+...+\dfrac{1}{6561}\right)\)

\(2A=\dfrac{6560}{6561}\)

\(A=\dfrac{3280}{6561}\)

\(A=\dfrac{3}{5.6}+\dfrac{3}{6.7}+...+\dfrac{3}{91.92}\)

\(\Rightarrow A=3\left(\dfrac{1}{5.6}+\dfrac{1}{6.7}+...+\dfrac{1}{91.92}\right)\)

\(\Rightarrow A=3\left(\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+...+\dfrac{1}{91}-\dfrac{1}{92}\right)\)

\(\Rightarrow A=3\left(\dfrac{1}{5}-\dfrac{1}{92}\right)\)

\(\Rightarrow A=3.\dfrac{87}{460}=\dfrac{261}{460}\)

(1/9+1/81) + 1/3+ 1/6561= 2998/6561 k xcho minh nha

=\(\frac{2187+729+81+1}{6561}\)= \(\frac{2998}{6561}\)

Sửa đề: A=1/3+1/9+1/27+...+1/6561

=1/3+1/3^2+1/3^3+...+1/3^8

=>3A=1+1/3+...+1/3^7

=>3A-A=1-1/3^8

=>\(2A=\dfrac{3^8-1}{3^8}\)

=>\(A=\dfrac{3^8-1}{2\cdot3^8}\)

Đặt \(S=\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{6561}\)

\(3S=1+\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{2187}\)

\(2S=\dfrac{2188}{2187}-\left(\dfrac{1}{27}+\dfrac{1}{6561}\right)\)

\(2S=\dfrac{2188}{2187}-\dfrac{244}{6561}\)

\(2S=\dfrac{4376}{6561}-\dfrac{244}{6561}\)

\(2S=\dfrac{4132}{6561}\)

\(S=\dfrac{2066}{6561}\)