Đáp án:
$A_{2}$ = `499/500`
Giải thích các bước giải:
$A_{2}$ `=` `1/( 1 . 2 )` `+` `1/(2 . 3 )` `+` `1/( 3 . 4 )` `+ ... +` `1/( 499 . 500)`
$A_{2}$ = `( 2 - 1 )/( 1 . 2 )` + `( 3 - 2 )/( 2 . 3 )` + `( 4 - 3 )/( 3 . 4 )` `+ ... +` `( 500 - 499 )/( 499 . 500 )`
$A_{2}$ `= 1` `-` `1/2` `+` `1/2` `-` `1/3` `+` `1/3` `-` `1/4` `+ ... +` `1/499` `-` `1/500`
$A_{2}$ `= 1 +` ( `-` `1/2` `+` `1/2` `-` `1/3` `+` `1/3` `-` `1/4` `+ ... +` `1/499` ) `-` `1/500`
$A_{2}$ `= 1 -` `1/500`
$A_{2}$ `=` `499/500`
Vậy $A_{2}$ `=` `499/500`