lim(n->inf)[3n^2+n]/[2n^2-1] = lim(n->inf)[3+1/n]/[2-1/n^2] = 3/2
【當(dāng)分子,分母都是無(wú)窮大時(shí).分子,分母同除以一個(gè)無(wú)窮大因子.使得分子,分母中至少有1個(gè)不再是無(wú)窮大.極限就出來(lái)了.】
lim(n->inf)[(3n)^2+n]/[(2n)^2-1] = lim(n->inf)[9+1/n]/[4-1/n^2] = 9/4
lim(n->inf)[1+1/2+...+1/2^n]/[1+1/4+...+1/4^n]
=lim(n->inf)[1-1/2^(n+1)]/(1-1/2)*(1-1/4)/[1-1/4^(n+1)]
=lim(n->inf)[1-1/2^(n+1)]/[1-1/4^(n+1)]*(4-1)/(4-2)
= 3/2
【分子,分母是無(wú)限項(xiàng)和時(shí).先分別求有限項(xiàng)和,再算極限】