|√(n+1)-√n -0| < ε
|1/(√(n+1) + √n )| < ε
1/(2√n)< ε
n > { 1/(2ε) }^2
∀ε>0 ,∃N = [{ 1/(2ε) }^2] +1, st
|√(n+1)-√n -0| < ε, ∀N>n
=>
lim(n->∞) [√(n+1)-√n]=0