Tính nhanh: \(\Large B = \dfrac{5}{2}+\dfrac{5}{6}+\dfrac{5}{18}+\dfra

Tính nhanh:

\(\Large B = \dfrac{5}{2}+\dfrac{5}{6}+\dfrac{5}{18}+\dfrac{5}{54}+\dfrac{5}{162}+\dfrac{5}{486}=...\)

( Viết đáp án đúng dưới dạng x/y)

• A. 910/243

Ta có :

\(\Large B = \dfrac{5}{2}+\dfrac{5}{6}+\dfrac{5}{18}+\dfrac{5}{54}+\dfrac{5}{162}+\dfrac{5}{486}\)

\(\Large 3\times B =3\times( \dfrac{5}{2}+\dfrac{5}{6}+\dfrac{5}{18}+\dfrac{5}{54}+\dfrac{5}{162}+\dfrac{5}{486})\)

\(\Large 3\times B = \dfrac{15}{2}+\dfrac{5}{2}+\dfrac{5}{6}+\dfrac{5}{18}+\dfrac{5}{54}+\dfrac{5}{162}\)

\(\Large 3\times B-B = (\dfrac{15}{2}+\dfrac{5}{2}+\dfrac{5}{6}+\dfrac{5}{18}+\dfrac{5}{54}+\dfrac{5}{162})-(\dfrac{5}{2}+\dfrac{5}{6}+\dfrac{5}{18}+\dfrac{5}{54}+\dfrac{5}{162}+\dfrac{5}{486})\)

\(\Large 2\times B= \dfrac{15}{2}-\dfrac{5}{486}\)

\(\Large 2\times B= \dfrac{3640}{486}=\dfrac{1820}{243}\)

\(\Large B=\dfrac{1820}{243}:2=\dfrac{910}{243}\)