limn趋近于无穷1/[2n(根号下n^2+1)-根号下(n^2-1)]是求极限的题...谢谢啦

Question

limn趋近于无穷1/[2n(根号下n^2+1)-根号下(n^2-1)]
是求极限的题...谢谢啦

Answer 1

1/2,
分子分母同乘[(根号下n^2+1)+根号下(n^2-1)]
因为[(根号下n^2+1)-根号下(n^2-1)][(根号下n^2+1)+根号下(n^2-1)]==2,
所以分母为4*n
则化成[(根号下n^2+1)+根号下(n^2-1)]/(4*n)
因为趋近于无穷,所以[(根号下n^2+1)+根号下(n^2-1)]趋近于2*n
比得1/2