Mathematics - Real Analysis - Sequences and series - Convergence of Sequences and Series

12 steps: (1) Sequence: ordered list a₁,a₂,a₃,... (2) Converges to L if for every ε>0, there exists N such that |aₙ-L|<ε for all n>N. (3) Examples: 1/n→0, (n+1)/n→1, 2ⁿ→∞ (diverges). (4) SERIES: sum of sequence terms. S=Σaₙ. (5) Partial sums: Sₙ=a₁+a₂+...+aₙ. Series converges if {Sₙ} converges. (6)