Question

lim┬(n→∞)⁡√(n)这个极限怎么求

Answer 1

求极限：lim(n→∞)[n-(√n*2+n)+1].

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

=(n^2-(n^2+n))/(n+√(n^2+n))+1

=-n/(n+√(n^2+n))+1

=1-1/(1+√(1+1/n))

所以：lim(n→∞)[n-√(n^2+n)+1]= lim(n→∞)[1-1/(1+√(1+1/n))]

=1-1/2

=1/2