• 421 First comparison test
ᐥIf 0 ≤ a⸤n⸥ ≤ b⸤n⸥ for all n∈ℕ then (a) ｢b⸤i⸥ Σi=1,∞｣ converges ⇒ ｢a⸤i⸥ Σi=1,∞｣ converges (b) ｢a⸤i⸥ Σi=1,∞｣ diverges ⇒ ｢b⸤i⸥ Σi=1,∞｣ divergesᐥ Proof of (a) ┆0 ≤ a⸤n⸥┆ ｢a⸤i⸥ Σi=1,n｣ is increasing. ｢a⸤i⸥ Σi=1,n｣ ┆a⸤n⸥ ≤ b⸤n⸥┆ ≤ ｢b⸤i⸥ Σi=1,n｣ ┆0 ≤ b⸤n⸥┆ ...
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