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Đặt `A = 1/4 + 1/16 + ... + 1/10000`
`->A = 1/2^2 + 1/4^2 + ... + 1/100^2`
Đặt `B = 1/4^2 + 1/6^2 + ... + 1/100^2`
Vì `4^2 > 2 . 4`
`-> 1/4^2 < 1/(2.4)`
Tương tự có :
`1/6^2 < 1/(4.6)`
`..........`
`1/100^2 < 1/(98 . 100)`
Cộng theo vế ta được :
`-> 1/4^2 + 1/6^2 + ... + 1/100^2 < 1/(2.4) + 1/(4.6)+...+1/(98 . 100)`
`-> B < 1/2 (1/2 - 1/4+1/4-1/6+...+1/98 - 1/100)`
`-> B < 1/2 (1/2 - 1/100)`
`-> B < 1/4 - 1/200`
`-> 1/2^2 + B < 1/2^2 + 1/4 - 1/200`
`-> A < 1/4 + 1/4 - 1/200`
`->A < 1/2 - 1/200`
Vì `1/2 -1/200 < 1/2`
`-> A < 1/2 - 1/200 < 1/2`
`-> A < 1/2` (đpcm)
