Question

求极限，n→∞

Answer 1

limxn=limn^2√(1-1/(n+1))-(n^2+1)√(1-1/(n+2))=limn^2-(n^2+1)=-1

追问

答案不对啊

答案不对啊

追答

=lim(n^5/(n+1)-(n^2+1)^2(n+1)/(n+2))/(n²√n/(n+1)+(n²+1)√(n+1)/(n+2))
=lim(n^5(n+2)-(n²+1)²(n+1)²)/(n²(n+2)√n(n+1)+(n²+1)(n+1)√(n+1)(n+2))
=lim(n^6+2n^5-(n³+n²+n+1)²)/(n²(n+2)√n(n+1)+(n²+1)(n+1)√(n+1)(n+2))
=lim(n^6+2n^5-(n^6+2n^5+3n^4+4n³+3n²+2n+1))/(n²(n+2)√n(n+1)+(n²+1)(n+1)√(n+1)(n+2))
=lim-(3+4/n+3/n²+2/n³+1/n^4)/((1+2/n)√(1+1/n)+(1+1/n²)(1+1/n)√(1+1/n)(1+2/n))
=-3/2