lim(n→∞)√n*[√(n+1)-√(n-1)]
=lim(n→∞)√n*[√(n+1)-√(n-1)]*[√(n+1)+√(n-1)]/[√(n+1)+√(n-1)]
=lim(n→∞)2√n/[√(n+1)+√(n-1)]
=lim(n→∞)2/[√(1+1/n)+√(1-1/n)]
=2/(1+1)
=1
lim(n→∞)√n*[√(n+1)-√(n-1)]
=lim(n→∞)√n*[√(n+1)-√(n-1)]*[√(n+1)+√(n-1)]/[√(n+1)+√(n-1)]
=lim(n→∞)2√n/[√(n+1)+√(n-1)]
=lim(n→∞)2/[√(1+1/n)+√(1-1/n)]
=2/(1+1)
=1