Alternating series and Leibniz test
General · Mathematics
Study notes
Q: Show Σ(-1)ⁿ⁺¹/n converges and estimate the sum using 3 terms. bₙ = 1/n: decreasing → 0 ✓: Leibniz: CONVERGES! Sum: ln 2 ≈ 0.693. 3 terms: 1 - 1/2 + 1/3 = 0.833. Error ≤ b₄ = 1/4 = 0.25. |0.833 - 0.693| = 0.14 ≤ 0.25 ✓ (error bound works!).