Read Theorem 5.12 in the textbook Links to an external site. .  Suppose 𝑎 𝑛 ≥ 0   for all 𝑛 ≥ 1 and 𝑏 𝑛 ≥ 0   for all 𝑛 ≥ 1 . a) If ∑ 𝑛 = 1 ∞ 𝑏 𝑛   converges and lim 𝑛 → ∞ 𝑎 𝑛 𝑏 𝑛 = 5   then   ∑ 𝑛 = 1 ∞ 𝑎 𝑛     [ Select ] might converge or diverge (there is not enough information) converges diverges   b) If ∑ 𝑛 = 1 ∞ 𝑏 𝑛   converges and lim 𝑛 → ∞ 𝑎 𝑛 𝑏 𝑛 = 0     then   ∑ 𝑛 = 1 ∞ 𝑎 𝑛     [ Select ] diverges converges might converge or diverge (there is not enough information)   c) If ∑ 𝑛 = 1 ∞ 𝑏 𝑛   diverges and lim 𝑛 → ∞ 𝑎 𝑛 𝑏 𝑛 = 0     then   ∑ 𝑛 = 1 ∞ 𝑎 𝑛     [ Select ] might converge or diverge (there is not enough information) diverges converges   d) If ∑ 𝑛 = 1 ∞ 𝑏 𝑛   diverges and lim 𝑛 → ∞ 𝑎 𝑛 𝑏 𝑛 = 200     then   ∑ 𝑛 = 1 ∞ 𝑎 𝑛     diverges