Question

Limn趋于无穷〔根号（n+2)-根号(n+1)+根号n]

Answer 1

lim[√(n+2) - √(n+1) + √n]

n→∞

∵lim[√(n+2) - √(n+1)]

n→∞

= lim[√(n+2)-√(n+1)][√(n+2)+√(n+1)]/[√(n+2)+√(n+1)] [分子有理化]

n→∞

= lim 1/[√(n+2)+√(n+1)]

n→∞

= 1/[√∞+√∞]

= 1/∞

= 0

∴lim[√(n+2) - √(n+1) + √n]

n→∞

= lim[0 + √n]

n→∞

= ∞