Question

Answer 1

`A = 2^100 - 2^99 + 2^98 - 2^97 + ... + 2^2 - 2`

`2A = 2^101 - 2^100 + 2^99 - 2^98 + ... + 2^3 - 2^2`

`2A + A = (2^101 - 2^100 + 2^99 - 2^98 + ... + 2^3 - 2^2) + (2^100 - 2^99 + 2^98 - 2^97 + ... + 2^2 - 2)`

`3A = 2^101 - 2`

`A = ( 2^101 - 2)/3`

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`B = 1/2 + 2/(2^2) + ... + 10/(2^10)`

`2B = 1 + 2/2 + ... + 10/(2^9)`

`2B - B = (1 + 2/2 + ... + 10/(2^9)) - (1/2 + 2/(2^2) + ... + 10/(2^10))`

`B = 1 + (2/2 - 1/2) + (3/(2^2) - 2/(2^2)) + ... + (10/(2^9) - 9/(2^9)) - 10/(2^10)`

`B = 1 - 10/(2^10)`

`B = (2^10 - 10)/(2^10)`

Answer 2

Sửa lại câu b

`B = 1/2 + 2/(2^2) + ... + 10/(2^10)`

`2B = 1 + 2/2 + ... + 10/(2^9)`

`2B - B = (1 + 2/2 + ... + 10/(2^9)) - (1/2 + 2/(2^2) + ... + 10/(2^10))`

`B = 1 + (2/2 - 1/2) + (3/(2^2) - 2/(2^2)) + ... + (10/(2^9) - 9/(2^9)) - 10/(2^10)`

`B = 1 + 1/2 + 1/(2^2) + ... + 1/(2^9) - 10/(2^10)`

`S = 1 + 1/2 + 1/(2^2) + ... + 1/(2^9)`

`2S = 2 + 1 + 1/2 + ... + 1/(2^8) `

`2S - S = (2 + 1 + 1/2 + ... + 1/(2^8) ) - (1 + 1/2 + 1/(2^2) + ... + 1/(2^9))`

`S = 2 - 1/(2^9)`

`B = 2 - 1/(2^9) - 10/(2^10)`

`B = (2^11 - 2 - 10)/(2^10)`

`B = (2^11 - 12)/(2^10)`