364/729

364/729

\(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)

\(=\frac{243}{729}+\frac{81}{729}+\frac{27}{729}+\frac{3}{729}\)

\(=\frac{243+81+27+3}{729}=\frac{354}{729}\)

1/3 + 1/9 + 1/27 + 1/81 + 1/243 +1/729 = 354/729

\(\frac{1}{3}\)+ \(\frac{1}{9}\)+ \(\frac{1}{27}\)+ \(\frac{1}{81}\)+ \(\frac{1}{243}\)+ \(\frac{1}{729}\)

= \(\frac{243}{729}\)+ \(\frac{81}{729}\)+ \(\frac{27}{729}\)+ \(\frac{9}{729}\)+ \(\frac{3}{729}\)+ \(\frac{1}{729}\)

= \(\frac{\left(243+27\right)+\left(81+9\right)+\left(3+1\right)}{729}\)

= \(\frac{270+90+4}{729}\)

=\(\frac{364}{729}\)

:)

Tính nhanh mà

chia ra từng cái một rồi tính

364/729

lấy MS chung là 2187, ta có:

        729 + 243 + 81 + 9 + 3 + 1                         

       ________________________  =      1066/2187

                      2187

1066/2187.

đặt S=\(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)

=>3S= \(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)

=>3S-S=\(\left(1+\frac{1}{3}+...+\frac{1}{243}\right)-\left(\frac{1}{3}+\frac{1}{9}+...+\frac{1}{729}\right)\)

=>s=1-1/729 = 728/729

1/3+1/9+1/27+1/81+1/243+1/729=(1/3+1/9+1/81)+(1/27+1/243+1/729)=37/81+37/729=333/729+37/729=370/729

 Đặt A = 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 
A x 3 = 3 x (1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729) 
= 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 
A x 3 - A = 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 - (1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729) 
= 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 - 1/3 - 1/9 - 1/27 - 1/81 - 1/243 - 1/729 
= 1 - 1/729 
A x 2 = 728/729 
A = 364/729

1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729

=1+ 243/729+ 81/729 + 27/729 + 9/729 + 3/729

=1093/729

1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729

=1093/729