a : N → R a(n) a n ∈ N a n n (a n ) n∈N (a n ) (a n ) n∈N M |a n | M n ∈ N a ∈ R (a n ) n∈N a = lim n→+∞ a n ε > 0 n 0 n > n 0 |a n − a| < ε a = +∞ (a n ) n∈N lim n→+∞ a n = +∞ M n 0 n > n 0 a n > M lim n→+∞ a n = −∞ M n 0 n > n 0 a n < M a = lim n→+∞ a n a ∈ R a = ±∞ (a n ) n∈N a n +∞ (a n ) n∈N a a a (a n ) n∈N a a = ±∞ (a n ) n∈N +∞ −∞ R (a n ) (b n ) lim n→+∞ a n = a lim n→+∞ b n = b 1 ◦ lim n→+∞ (a n ± b n ) = a ± b 2 ◦ lim n→+∞ (a n b n ) = ab 3 ◦ lim n→+∞ a n b n = a b b n = 0 n ∈ N b = 0