lim(1+4+7+…+(3n-2))/(7n^2-5n),

lim(1+4+7+…+(3n-2))/(7n^2-5n),

等差數列求和
1+4+7+…+(3n-2)=[1+(3n-2)]n/2=(3n^2-n)/2
lim(1+4+7+…+(3n-2))/(7n^2-5n)
=lim(3n^2-n)/(14n^2-10n)
=3/14