Math Problem Statement
Test for convergence for question (d) and (e)
Solution
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Math Problem Analysis
Mathematical Concepts
Alternating Series Test
Limit Comparison Test
p-Series
Formulas
Alternating Series Test: ∑ (-1)^n b_n converges if b_n is positive, decreasing, and lim (n → ∞) b_n = 0
Limit Comparison Test: lim (n → ∞) (a_n / b_n) = L, where L > 0
p-Series: ∑ 1/n^p converges if p > 1, diverges if p ≤ 1
Theorems
Leibniz Criterion
Limit Comparison Test
p-Series Theorem
Suitable Grade Level
Grades 11-12 (Advanced High School/Introductory College Level)