lim(n→∞) （n+1）(n+2) (n+3)/5n3次方+n 的极限?

lim(n→∞) (n+1)(n+2)(n+3)/(5n³+n)
=lim(n→∞) (1+1/n)(1+2/n)(1+3/n)/(5+1/n²) .分子分母同时除以n³
=1/5

lim(n→∞) （n+1）(n+2) (n+3)/5n3次方+n
=lim(n→∞) （n^2+3n+2) (n+3)/(5n3次方+n)
=lim(n→∞) （n^3+3n^2+3n^2+6n+2n+6)/5n3次方+n
=lim(n→∞) （n^3+6n^2+8n+6)/5n3次方+n
=lim(n→∞) （1+6/n+8/n^2+6/n^3)/(5+1/n^2)
=1/5