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[tex]\lim_{n \to \infty} (\sqrt{n+1}-\sqrt{n} ),[/tex]
[tex]\lim_{n \to \infty} (\sqrt{n+1}-\sqrt{n} ),[/tex]
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lim(n->∞) (√(n + 1) - √n) = lim(n->∞) (√(n + 1) - √n) * (√(n + 1) +√n) / (√(n + 1) + √n) = lim(n->∞) ((n + 1) - n) / (√(n + 1) + √n) = lim(n->∞) ( 1 / (√(n + 1) + √n) = 1/(∞ + ∞) = 0