\(\frac{1}{9}\)Lớn hơn nhé !

bn tự giải nhé tớ gợi ý cho bn nè 

gộp các số bị trừ vào 1 cặp và tất cả số trừ vào 1 cặp

\(\frac{1}{9}>A\)

Kết bạn với mình nha!

Ta có:

\(A=\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{17}-\dfrac{1}{31}+\dfrac{1}{65}-\dfrac{1}{127}\)

\(A=\dfrac{2}{35}+\dfrac{14}{527}+\dfrac{62}{8255}\)

\(A=0.09121892168\)

Vì \(\dfrac{1}{9}=0.1111111111\)

Nên \(A< \dfrac{1}{9}\)

Vậy \(A< \dfrac{1}{9}\).

4: \(=\dfrac{2+3}{7}+\dfrac{1+6}{9}-\dfrac{5}{6}=\dfrac{5}{7}+\dfrac{7}{9}-\dfrac{5}{6}=\dfrac{83}{126}\)

5: \(=\dfrac{-5-2}{7}+\dfrac{3+1}{4}-\dfrac{1}{5}=-\dfrac{1}{5}\)

6: \(=\dfrac{-3-28}{31}+\dfrac{-6-1}{17}+\dfrac{1-5}{25}=-1-\dfrac{7}{17}-\dfrac{4}{25}=-\dfrac{668}{425}\)

4. \(\dfrac{2}{7}+\dfrac{1}{9}+\dfrac{3}{7}+\dfrac{5}{9}+\dfrac{-5}{6}\)

\(=\left(\dfrac{2}{7}+\dfrac{3}{7}\right)+\left(\dfrac{1}{9}+\dfrac{5}{9}\right)+\dfrac{-5}{6}\)

\(=\dfrac{5}{7}+\dfrac{2}{3}+\dfrac{-5}{6}\)

\(=\dfrac{30+28+\left(-35\right)}{42}=\dfrac{23}{42}\)
 

5. \(\dfrac{-5}{7}+\dfrac{3}{4}+\dfrac{-1}{5}+\dfrac{-2}{7}+\dfrac{1}{4}\)

\(=\left(\dfrac{-5}{7}+\dfrac{-2}{7}\right)+\left(\dfrac{3}{4}+\dfrac{1}{4}\right)+\dfrac{-1}{5}\)

\(=\dfrac{-7}{7}+\dfrac{4}{4}+\dfrac{-1}{5}\)

\(=-1+1+\dfrac{-1}{5}\)

\(=-\dfrac{1}{5}\)
 

6. \(\dfrac{-3}{31}+\dfrac{-6}{17}+\dfrac{1}{25}+\dfrac{-28}{31}+\dfrac{-1}{17}+\dfrac{-1}{5}\)

\(=\left(\dfrac{-3}{31}+\dfrac{-28}{31}\right)+\left(\dfrac{-6}{17}+\dfrac{-1}{17}\right)+\dfrac{1}{25}+\dfrac{-1}{5}\)

\(=\dfrac{-31}{31}+\dfrac{-7}{17}+\dfrac{1}{25}+\dfrac{-1}{5}\)

\(=-1+\dfrac{-7}{17}+\dfrac{1}{25}+\dfrac{-1}{5}\)

\(=\dfrac{-425+\left(-175\right)+17+\left(-85\right)}{425}=\dfrac{-668}{425}\)

1/3+1/5+1/9+1/17+1/35+1/65+1/129+1/259

=(1/3+1/5)+(1/9+1/17)+(1/35+1/65)+(1/129+258)

< (1/3) . 2 + (1 / 8) . 2 +(1/32 .2)+(1/128).2 = 2/3 + 1/4 + 1/16+1/64=2/3+16/64+4/64+1/64=2/3+21/64=191/192 < 1

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