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The results of limits of a some simple sequences is obvious if put a few first natural numbers to formulas like in these examples. lim_{n → ∞} n = ∞; for 3n^2, 5n^3, 8n^5, n^7, ... too ∞. lim_{n → ∞} (-n) = -∞; for -3n^2, -5n^3, -8n^5, -n^7, ... too -∞. lim_{n → ∞} 1/n = 0; -2/n, 3/n^2, 8/n, -9/n^3,... too 0. If a * 1 then lim_{n → ∞} a^n = ∞; lim_{n → ∞} 2^n = ∞; for 8^n, 2^n, (1 1/3)^n, (5/4)^n,... too ∞. If |a| * 1 then lim_{n → ∞} a^n = 0; lim_{n → ∞} (1/2)^n = 0; for (-2/3)^n, (0.3)^n, -(3/5)^n, 4/7^n,... too 0.