Tính A=1+2.6+3.6^2+4.6^3+…+51.6^50

1 bình luận về “Tính A=1+2.6+3.6^2+4.6^3+…+51.6^50”

1. A=1+2.6+3.6^2+4.6^3+…+51.6^{50}

   =>6A=6+2.6^2+3.6^3+…+51.6^{51}

   =>6A-A=(6+2.6^2+3.6^3+..+51.6^{51})-(1+2.6+3.6^2+4.6^3+…+51.6^{50})

   =>5A=51.6^{51}-1-6-6^2-6^3-…-6^{50}

   =51.6^{51}-1-(6+6^2+6^3+…+6^{50}

   Đặt B=6+6^2+6^3+…+6^{50}

   =>6B=6^2+6^3+6^4+…+6^{51}

   =>6B-B=(6^2+6^3+6^4+…+6^{51})-(6+6^2+6^3+…+6^{50})

   =>5B=6^{51}-6 

   =>B=(6^{51}-6)/5

   =>A=51.6^{51}-1-(6^{51}-6)/5

   =(51.6^{51}.5-5+6^{51}-6)/5

   =(256.6^{51}-11)/5

    

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