Tính A= 1/5^2 + 2/5^3 + 3/5^4 +…+ 11/5^12

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1. Giải thích các bước giải:

   `A= 1/5^2 + 2/5^3 + 3/5^4 +…+ 11/5^12`

   `5A= 1/5 + 2/5^2 + 3/5^3 +…+ 11/5^11`

   `5A-A=(1/5 + 2/5^2 + 3/5^3 +…+ 11/5^11)-(1/5^2 + 2/5^3 + 3/5^4 +…+ 11/5^12)`

   `4A=1/5 + 1/5^2 + 1/5^3 +…+ 1/5^11-11/5^12`

   Đặt `B=1/5 + 1/5^2 + 1/5^3 +…+ 1/5^11`

   `5B=5 + 1/5 + 1/5^2 +…+ 1/5^10`

   `5B-B=(5 + 1/5 + 1/5^2 +…+ 1/5^10)-(1/5 + 1/5^2 + 1/5^3 +…+ 1/5^11)`

   `4B=5-1/5^11`

   `B=(5-1/5^11)/4`

   `=>4A=(5-1/5^11)/4-11/5^12`

   `=>A=((5-5/5^12)/4-11/5^12)/4=((5-49)/5^12)/4=-44/(4.5^12)=-11/5^12`

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