Mathematics - Real Analysis - Sequences and series - Convergence Tests

10 problems: (1-2) Does the sequence converge? (2n)/(3n+1), (-1)ⁿ·n/(n+1). (3-4) Geometric series: find sum of Σ(1/3)ⁿ, Σ2·(0.7)ⁿ. (5) p-series: does Σ1/n³ converge? Σ1/√n? (6-7) Ratio test: Σn!/nⁿ, Σ3ⁿ/n!. (8) Comparison test: Σ1/(n²+1) compared to Σ1/n². (9) Alternating: does Σ(-1)ⁿ/n converge? Ab