數(shù)列a1,a2,...,an,...有極限A,數(shù)列b1,b2,...,bn,...也有極限B
極限乘法運(yùn)算律：lim(an*bn)=lim(an)*lim(bn)=A*B
證明：
anbn-AB=(an-A)(bn-B)+B(an-A)+A(bn-B)
對(duì)任意εN₁時(shí),有|B||an-A|N₂時(shí),有|A||bn-B|N=Max(N₁,N₂)時(shí),有|an-A||bn-B|