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

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

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

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

Đặt \(V=\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}+...+\dfrac{1}{729}+\dfrac{1}{2187}\)

\(\Rightarrow3V=3.\left(\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}+...+\dfrac{1}{729}+\dfrac{1}{2187}\right)\)

\(\Rightarrow3V=1+\left(\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}+...+\dfrac{1}{729}\right)\)

\(\Rightarrow3V=1+V-\dfrac{1}{2187}\)

\(\Rightarrow2V=1-\dfrac{1}{2187}\)

\(\Rightarrow V=\dfrac{1093}{2187}\).

1093/2187 nha bạn

A= 1/3 + 1/9 + 1/27 + 1/81 +...+1/729 + 1/2187

3A = 1 + 1/3 + 1/9 + 1/27 + 1/81 +...+1/729 

=> 3A - A = 1 - 1/2187

đề sai à

link j bạn

S = 1 + 1/3 + 1/9 + 1/27 +.....+ 1/2187

S x 3 = 3 + 1 + 1/3 + 1/9 + 1/27 +........+ 1/729

S x 3 - S = ( 3 + 1 + 1/3 + 1/9 + 1/27 +........+ 1/729 ) - ( 1 + 1/3 + 1/9 + 1/27 +.....+ 1/2187 )

S x 3 - S = 3 - 1/2187

S x 3 - S = 6560/2187

S = 6560/2187 : 2

Vậy S = 6560/4374

lấy MS chung là 2187, ta có:

        729 + 243 + 81 + 9 + 3 + 1                         

       ________________________  =      1066/2187

                      2187

1066/2187.

<=>3x+9x+27x+81x+243x+729x+2187x = 9837

<=>3279 x = 9837

<=>x=3

S = 1 + \(\frac{1}{3}\)+ \(\frac{1}{9}\)+ \(\frac{1}{27}\)+...+ \(\frac{1}{2187}\)

3S = 3 + 1 + \(\frac{1}{3}\)+ \(\frac{1}{9}\)+...+ \(\frac{1}{729}\)

3S - S = 3 - \(\frac{1}{2187}\)

2S = \(\frac{6560}{2187}\)

S = \(\frac{6560}{2187}\): 2

S = \(\frac{6560}{4374}\)

thay 1thành 3/3,1/3 thành 1/3¹,1/9 thành 1/3²,1/27 thành 1/3³,rồi cứ thế tiếp tục

xong rồi thì cộng lại như phân số

\(A=\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+...+\dfrac{1}{2187}+\dfrac{1}{6561}\)

\(3A=1+\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+...+\dfrac{1}{2187}\)

Lấy 3A - A ta được :

\(2A=1-\dfrac{1}{6561}=\dfrac{6560}{6561}\Leftrightarrow A=\dfrac{6560}{6561}:2\)

\(\Leftrightarrow A=\dfrac{6560}{6561}.\dfrac{1}{2}=\dfrac{3280}{6561}\)