Lời giải:
`1-1/2+1/3-1/4+....+1/2010`
`=1-1/3+1/4+....+1/2009-(1/2+1/4+...+1/2010)`
`=1+1/2+1/3+....+1/2010-2(1/2+1/4+...+1/2010)`
`=1+1/2+1/3+....+1/2010-(1+1/2+...+1/2005)`
`=1/1006+1/1007+...+1/2010`
`=>`
`(1/1006+1/1007+...+1/2010)/(1-1/2+1/3-1/4+....+1/2010)`
`=(1/1006+1/1007+...+1/2010)/(1/1006+1/1007+...+1/2010)`
`=1`
Vậy `A=1`