lim[(2n+3)/(2n+2)]^(n), n趋向无穷大,求极限。
2个回答
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解：
lim [(2n+3)/(2n+2)]ⁿ
n→∞
=lim [(2n+2+1)/(2n+2)]ⁿ
n→∞
=lim [1+ 1/(2n+2)]ⁿ
n→∞
=lim {[1+ 1/(2n+2)]²ⁿ⁺²}^(½) ·[1+ 1/(2n+2)]⁻¹
n→∞
=e^(½)· (1+0)⁻¹
=√e·1
=√e
lim [(2n+3)/(2n+2)]ⁿ
n→∞
=lim [(2n+2+1)/(2n+2)]ⁿ
n→∞
=lim [1+ 1/(2n+2)]ⁿ
n→∞
=lim {[1+ 1/(2n+2)]²ⁿ⁺²}^(½) ·[1+ 1/(2n+2)]⁻¹
n→∞
=e^(½)· (1+0)⁻¹
=√e·1
=√e
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引用xuzhouliuying的回答：
解：
lim [(2n+3)/(2n+2)]ⁿ
n→∞
=lim [(2n+2+1)/(2n+2)]ⁿ
n→∞
=lim [1+ 1/(2n+2)]ⁿ
n→∞
=lim {[1+ 1/(2n+2)]²ⁿ⁺²}^(½) ·[1+ 1/(2n+2)]⁻¹
n→∞
=e^(½)· (1+0)⁻¹
=√e·1
=√e
解：
lim [(2n+3)/(2n+2)]ⁿ
n→∞
=lim [(2n+2+1)/(2n+2)]ⁿ
n→∞
=lim [1+ 1/(2n+2)]ⁿ
n→∞
=lim {[1+ 1/(2n+2)]²ⁿ⁺²}^(½) ·[1+ 1/(2n+2)]⁻¹
n→∞
=e^(½)· (1+0)⁻¹
=√e·1
=√e
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lim [(2n+3)/(2n+2)]ⁿ
n→∞
=lim [(2n+2+1)/(2n+2)]ⁿ
n→∞
=lim [1+ 1]ⁿ n→∞
=2
n→∞
=lim [(2n+2+1)/(2n+2)]ⁿ
n→∞
=lim [1+ 1]ⁿ n→∞
=2
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