Mathematics - Real Analysis - Convergence and divergence - Prove Convergence

8 problems: (1) Write the ε-N definition of lim(n→∞) aₙ = L. (2) Prove lim(1/n²)=0 using ε-N definition. (Choose N>1/√ε). (3) Show {1/n} is Cauchy. (4) Determine: Σ(-1)ⁿ/n is absolutely or conditionally convergent? (Conditional). (5) Σ(-1)ⁿ/n² is absolutely or conditionally convergent? (Absolute). (