9.999999998 đoán vậy

1066/2187

Ta có \(H=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+....+\frac{1}{2187}\)

Suy ra \(3H=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+....+\frac{1}{729}\)

Nên \(3H-H=1-\frac{1}{2187}\)hay \(2H=1-\frac{1}{2187}\)

Do đó \(H=\frac{1}{2}-\frac{1}{4374}=\frac{1093}{2187}\)

Vậy \(H=\frac{1093}{2187}\)

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

\(\Rightarrow3B=3.\left(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+...+\frac{1}{2187}\right)\)

\(\Rightarrow3B=3+1+\frac{1}{3}+\frac{1}{9}+...+\frac{1}{729}\)

\(\Rightarrow3B-B=\left(3+1+\frac{1}{3}+\frac{1}{9}+...+\frac{1}{729}\right)-\)\(\left(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+...+\frac{1}{2187}\right)\)

\(\Rightarrow2B=3-\frac{1}{2187}\)

\(\Rightarrow B=\left(3-\frac{1}{2187}\right):2\)

\(\Rightarrow B=\frac{6560}{2187}\)

Chắc sai !!!

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

          = \(1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^7}\) 

3A = \(3+1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^6}\)

Lấy 3A - A = \(\left(3+1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^6}\right)-\left(1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^7}\right)\)

            2A   = \(3+1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^6}-1-\frac{1}{3}-\frac{1}{3^2}-\frac{1}{3^3}-...-\frac{1}{3^7}\)

            2A    = \(3-\frac{1}{3^7}\)

              A     = \(\left(3-\frac{1}{3^7}\right):2\)

\(\Rightarrow1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+...+\frac{1}{2187}=\left(3-\frac{1}{3^7}\right):2\)

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

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

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

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

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

1+3+9+27+....+2187+6561