数列极限.第二题
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数列极限.第二题
数列极限.第二题
数列极限.第二题
lim【n→∞】[2n+(an²-2n+1)/(bn+2)]
=lim【n→∞】{[2n(bn+2)+an²-2n+1]/(bn+2)}
=lim【n→∞】[(2bn²+4n+an²-2n+1)/(bn+2)]
=lim【n→∞】{[(a+2b)n²+2n+1]/(bn+2)}
这是一个∞/∞型的极限,应用...
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lim【n→∞】[2n+(an²-2n+1)/(bn+2)]
=lim【n→∞】{[2n(bn+2)+an²-2n+1]/(bn+2)}
=lim【n→∞】[(2bn²+4n+an²-2n+1)/(bn+2)]
=lim【n→∞】{[(a+2b)n²+2n+1]/(bn+2)}
这是一个∞/∞型的极限,应用洛比达法则,有:
lim【n→∞】{[(a+2b)n²+2n+1]/(bn+2)}
=lim【n→∞】{[2(a+2b)n+2]/b}
=2lim【n→∞】{[(a+2b)n+1]/b}
已知:lim【n→∞】[2n+(an²-2n+1)/(bn+2)]=1
即:2lim【n→∞】{[(a+2b)n+1]/b}=1
lim【n→∞】{[(a+2b)n+1]/b}=1/2
显然有:a+2b=0……………………(1)
代入极限,有:
lim【n→∞】(1/b)=1/2
1/b=1/2,解得:b=2
代入(1),有:a+2×2=0,解得:a=-4
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