a)
`A= ((1,5 +1-0,75)/(2,5 +5/3 -1,25) + (0,375-0,3+3/11+3/12)/(-0,625+0,5-5/11-5/12)) : 1890/2005 + 115`
`A= ((3/2+ 3/3 - 3/4)/(5/2 + 5/3-5/4) + (3/8-3/10+3/11+3/12)/(-5/8+5/10-5/11-5/12)) : 1890/2005 +115`
`A= (3(1/2+1/3-1/4))/(5(1/2+1/3-1/4)) + (3(1/8-1/10+1/11+1/12))/(-5(1/8-1/10+1/11+1/12)) : 1890/2005 + 115`
`A= 3/5 + (-3/5) : 1890/2005 + 115`
`A= 0. 2005/1890 + 115`
`A= 0 + 115`
`A= 115`
Vậy `A= 115`
b) `B = 1/3 + 1/3^2 + 1/3^3 + ...+ 1/3^2005`
`1/3 B = 1/3 ( 1/3 + 1/3^2 + 1/3^3 + ...+ 1/3^2005)`
`1/3 B= 1/3^2 + 1/3^3 +....+1/3^2006`
`B - 1/3 B = 1/3 + 1/3^2 + 1/3^3 +...+1/3^2005 - 1/3^2 - 1/3^3-....-1/3^2006`
`2/3 B = 1/3 - 1/3^2006`
`B = (1/3 - 1/3^2006) : 2/3`
`B = (1/3 - 1/3^2006) . 3/2`
`B= 1/3 . 3/2 - 1/3^2006 . 3/2`
`B= 1/2 - 1/(3^2005 .2) < 1/2`
Vậy `B < 1/2`
