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`