跪求速度呐!已知｛xn｝,｛yn｝满足lim(2xn+yn)=1,lim(xn-2yn)=1,求lim(xn*yn)的值.

Question

跪求速度呐!已知｛xn｝,｛yn｝满足lim(2xn+yn)=1,lim(xn-2yn)=1,求lim(xn*yn)的值.

Answer 1

lim(2xn+yn)=1,(1)
lim(xn-2yn)=1,(2)
所以-2*(2)得
-2*lim(xn-2yn)=-2*1=-2
lim(-2xn+4yn)=-2,(3)
(1)+(3),得
lim(2xn+yn)+(-2xn+4yn)=1+(-2)=-1
lim5yn=-1
limyn=-1/5
从而
lim(2xn+yn)-limyn=lim[(2xn+yn)-yn]=lim2xn=1-(-1/5)=6/5
所以
limxn=3/5
从而
lim(xn*yn)=limxn*limyn=3/5*(-1/5)=-3/25.