Đáp án + giải thích bước giải :
`S = 1/2^2 - 1/2^4 + 1/2^6 - ... + 1/2^{4n - 2} - 1/2^{4n} + ... + 1/2^{2002} - 1/2^{2004}`
`-> 2^2S = 1 -1/2^2 + 1/2^4 + ... + 1/2^{4n -4} - 1/2^{4n -2} + ... + 2/2^{2000} - 1/2^{2002}`
`-> 4S + S = (1 -1/2^2 + 1/2^4 + ... + 1/2^{4n -4} - 1/2^{4n -2} + ... + 2/2^{2000} - 1/2^{2002}) + (1/2^2 - 1/2^4 + 1/2^6 - ... + 1/2^{4n - 2} - 1/2^{4n} + ... + 1/2^{2002} - 1/2^{2004})`
`-> 5S = 1 - 1/2^{2004}`
Ta thấy : `1 - 1/2^{2004} < 1`
`-> 5S = 1 - 1/2^{2004} < 1`
`-> S = 1 - 1/2^{2004} < 1/5`
`-> S = 1 - 1/2^{2004} < 0,2`
hay `S < 0,2 (đpcm)`
