Tính nhanh: \(\Large E = \dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfra

Tính nhanh: 

\(\Large E = \dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}+\dfrac{1}{243}+\dfrac{1}{729}\)

Đáp án: \(\Large E = .....\)

• A.

  \(\Large \dfrac{364}{729}\)

• B.

  \(\Large \dfrac{114}{136}\)

• C.

  \(\Large \dfrac{345}{276}\)

• D.

  \(\Large \dfrac{264}{726}\)

Ta có:

\(\Large E = \dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}+\dfrac{1}{243}+\dfrac{1}{729}\)

\(\Large 3\times E = 3\times(\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}+\dfrac{1}{243}+\dfrac{1}{729})\)

\(\Large 3\times E= 1+\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}+\dfrac{1}{243}\)

\(\Large 3\times E-E= (1+\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}+\dfrac{1}{243})-( \dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}+\dfrac{1}{243}+\dfrac{1}{729})\)

\(\Large 2\times E= 1-\dfrac{1}{729}\)

\(\Large 2\times E=\dfrac{728}{729}\)

\(\Large E=\dfrac{728}{729}:2=\dfrac{364}{729}\)