Đáp án:
`A<13/400`
Giải thích các bước giải:
`A=3/5^3+4/5^4+5/5^5+...+102/5^102+103/5^103`
`=>5A=3/5^2+4/5^3+5/5^4+......+102/5^101+103/5^102`
`=>5A-A=3/5^2+1/5^3+1/5^4+.......+1/5^101-102/5^102`
`=>4A=3/5^2+1/5^3+1/5^4+.......+1/5^101-102/5^102`
`=>4A.5=3/5+1/5^2+1/5^3+.......+1/5^100-102/5^101`
`=>20A=3/5+1/5^2+1/5^3+.......+1/5^100-102/5^101`
`=>20A-4A=3/5-2/5^2-1/5^101-102/5^101`
`=>16A=3/5-2/5^2-1/5^101-102/5^101`
`=>16A<3/5-2/5^2`
`=>16A<13/25`
`=>A<13/400(ĐPCM)`
$@Kate2007$