求问第4、5、6题
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4题limxn=lim(1-a^(2^(n+1)))/(1-a)=1/(1-a)
5题limxn=(n^5/(n+1)-(n^2+1)^2(n+1)/(n+2))/(n^2√(1-1/(n+1))+(n^2+1)√(1-1/(n+2))
=lim(n^5(n+2)-(n^2+1)^2(n+1)^2)/(n^2√(1-1/(n+1))+(n^2+1)√(1-1/(n+2))(n+1)(n+2)
=lim(-3n^4-4n^3-3n^2-2n-1)/(n^2√(1-1/(n+1))+(n^2+1)√(1-1/(n+2))(n+1)(n+2)
=lim(-3-4/n-3/n^2-2/n^3-1/n^4)/(√(1-1/(n+1))+(1+1/n^2)√(1-1/(n+2))(1+1/n)(1+2/n)
=-3/2
6题limxn=lim(n^2-(n^2+2n))/(n+√(n^2+n))-1=lim-2/(1+√(1+1/n))-1=-2
5题limxn=(n^5/(n+1)-(n^2+1)^2(n+1)/(n+2))/(n^2√(1-1/(n+1))+(n^2+1)√(1-1/(n+2))
=lim(n^5(n+2)-(n^2+1)^2(n+1)^2)/(n^2√(1-1/(n+1))+(n^2+1)√(1-1/(n+2))(n+1)(n+2)
=lim(-3n^4-4n^3-3n^2-2n-1)/(n^2√(1-1/(n+1))+(n^2+1)√(1-1/(n+2))(n+1)(n+2)
=lim(-3-4/n-3/n^2-2/n^3-1/n^4)/(√(1-1/(n+1))+(1+1/n^2)√(1-1/(n+2))(1+1/n)(1+2/n)
=-3/2
6题limxn=lim(n^2-(n^2+2n))/(n+√(n^2+n))-1=lim-2/(1+√(1+1/n))-1=-2
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