jess8180 jess8180

06-03-2024
Mathematics

contestada

Consider the following list conjectures. Provide a short proof for those that are true and a counterexample for any that are false.
a) If lim (aₙ −bₙ )=0, then lim aₙ = lim bₙ .
b) If (bₙ )→b, then ∣bₙ ∣→∣b∣.
c) If (aₙ )→0 and (bₙ −aₙ )→0, then (b )→0.
d) If (aₙ )→0 and ∣bₙ −b∣ ≤ aₙ ∀n∈N, then(bₙ )→b.

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