Which fraction is greater: 333...331/333...334 or 222...221/222...223?

[anemone]

Which of the fractions is greater?

$$A=\frac{\overbrace{333\cdots331}^{ \large{\text{2012 pieces}}}}{\underbrace{333\cdots334}_{ \large{\text{2012 pieces}}}}$$

or

$$B=\frac{\overbrace{222\cdots221}^{ \large{\text{2012 pieces}}}}{\underbrace{222\cdots223}_{ \large{\text{2012 pieces}}}}$$?

 

[M R]

$$A=1-\frac{1}{33...34/3}=1-\frac{1}{111..11 +\frac{1}{3}}$$

$$B=1-\frac{1}{22...23/2}=1-\frac{1}{111..11+\frac{1}{2}}$$

B is greater.

 

[anemone]

Very beautiful and impressive, M R!(Clapping)