求极限题,求详细过程
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{[2(n+1)!]/[(n+1)!]^2}/[(2n)!/(n!)^2]
=(2n+2)!/(2n)!*[n!/(n+1)!]^2
=(2n+1)(2n+2)*1/(n+1)^2
=(4n+2)/(n+1)
所以原式=lim(x→∞)|(4n+2)/(n+1)*x^2|
=lim(x→∞)|(4+2/n)/(1+1/n)*x^2|
=(4+0)/(1+0)*x^2
=4x^2
=(2n+2)!/(2n)!*[n!/(n+1)!]^2
=(2n+1)(2n+2)*1/(n+1)^2
=(4n+2)/(n+1)
所以原式=lim(x→∞)|(4n+2)/(n+1)*x^2|
=lim(x→∞)|(4+2/n)/(1+1/n)*x^2|
=(4+0)/(1+0)*x^2
=4x^2
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