$\text { Đáp án: }$
$\text { Đặt }$ ` 1/2 + 1/4 + 1/8 + ... + 1/1042 ` $\text { là }$ ` A. `
$\text { Ta có: }$
` A = 1/2 + 1/4 + 1/8 + ... + 1/1042 `
` <=> 2A = 1 + 1/2 + 1/4 + ... + 1/521 `
` <=> 2A – A = ( 1 + 1/2 + 1/4 + ... + 1/521 ) – ( 1/2 + 1/4 + 1/8 + ... + 1/1042 ) `
` <=> A = 1 + 1/2 + 1/4 + ... + 1/521 – 1/2 – 1/4 – 1/8 – ... – 1/1042 `
` <=> A = 1 + ( 1/2 – 1/2 ) + ( 1/4 – 1/4 ) + ... + ( 1/521 – 1/521 ) + 1/1042 `
` <=> A = 1 + 1/1042 `
` <=> A = 1042/1042 + 1/1042 `
` <=> A = 1043/1042 `
$\text { Vậy }$ ` 1/2 + 1/4 + 1/8 + ... + 1/1042 = 1043/1042 `
