`A=5+5^2+5^3+…+5^1010` `B=4+4^2+4^3+…+4^180` `C=7+7^2+7^3+…+7^100`

2 bình luận về “`A=5+5^2+5^3+…+5^1010` `B=4+4^2+4^3+…+4^180` `C=7+7^2+7^3+…+7^100`”

1. A=5+5^2+5^3+..+5^1010

   =>5A=5^2+5^3+5^4+…+5^1011

   =>5A-A=(5^2+5^3+5^4+…+5^1011)-(5+5^2+5^3+…+5^1010)

   =>4A=5^1011-5

   =>A=(5^1011-5)/4

   ——–

   B=4+4^2+4^3+…+4^180

   =>4B=4^2+4^3+4^4+…+4^181

   =>4B-B=(4^2+4^3+4^4+…+4^181)-(4+4^2+4^3+…+4^180)

   =>3B=4^181-4

   =>B=(4^181-4)/3

   ——–

   C=7+7^2+7^3+…+7^100

   =>7C=7^2+7^3+7^4+…+7^101

   =>7C-C=(7^2+7^3+7^4+…+7^101)-(7+7^2+7^3+…+7^100)

   =>6C=7^101-7

   =>C=(7^101-7)/6

   Trả lời
2. A=5+5^2+5^3+..+5^{1010}

   =>5A=5^2+5^3+5^4+…+5^{1011}

   =>5A-A=(5^2+5^3+5^4+…+5^{1011})-(5+5^2+5^3+…+5^{1010})

   =>4A=5^{1011}-5

   =>A=(5^{1011}-5)/4

   B=4+4^2+4^3+…+4^{180}

   =>4B=4^2+4^3+4^4+…+4^{181}

   =>4B-B=(4^2+4^3+4^4+…+4^{181})-(4+4^2+4^3+…+4^{180})

   =>3B=4^{181}-4

   =>B=(4^{181}-4)/3

   C=7+7^2+7^3+…+7^{100}

   =>7C=7^2+7^3+7^4+…+7^{101}

   =>7C-C=(7^2+7^3+7^4+…+7^{101})-(7+7^2+7^3+…+7^{100})

   =>6C=7^{101}-7

   =>C=(7^{101}-7)/6

    

   Trả lời