Bài 1:
`A= 1 + 1/2 + 1/2^2 +1/2^3+...+1/2^2012`
`1/2 A= 1/2 ( 1+ 1/2+ 1/2^2 + 1/2^3+...+1/2^2012)`
`1/2 A= 1/2 + 1/2^2 + 1/2^3+...+1/2^2013`
`A- 1/2 A= 1+ 1/2 + 1/2^2 + 1/2^3 +...+1/2^2012 - 1/2 - 1/2^2 - 1/2^3 -...-1/2^2013`
`1/2A= 1- 1/2^2013`
`A= ( 1-1/2^2013) : 1/2`
`A= (1- 1/2^2013). 2`
`A= 2 - 1/2^2012`
Vậy `A= 2 - 1/2^2012`
Bài 2:
`A= (20^10 +1)/(20^10 -1)`
`A= (20^10 -1 +2)/(20^10-1)`
`A= (20^10-1)/(20^10 -1) + 2/(20^10 -1)`
`A= 1 + 2/(20^10 -1)`
`B= (20^10 -1)/(20^10 -3)`
`B= (20^10 -3 + 2)/(20^10 -3)`
`B= (20^10 -3)/(20^10 -3) + 2/(20^10-3)`
`B= 1 + 2/(20^10 -3)`
Vì `2/(20^10 -1) < 2/(20^10 -3)`
`=> 1 + 2/(20^10 -1) < 1 + 2/(20^10-3)`
`=> A < B`
Vậy `A<B`
