CHO A=1+4+4^2+4^3+………+4^98+4^99.B=4^100.Cmr A<B/3

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CHO A=1+4+4^2+4^3+………+4^98+4^99.B=4^100.Cmr A<B/3

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    `A=1+4+4^2+4^3+…+4^98+4^99`

    `=>` `4A=4+4^2+4^3+4^4+…+4^99+4^100`

    `=>` `3A=4A-A`

    `=(4+4^2+4^3+4^4+…+4^99+4^100)-(1+4+4^2+4^3+…+4^98+4^99)`

    `=4^100-1`

    `=>` `A=(4^100-1)/3=B/3-1/3 < B/3`

    `=>` đpcm

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