1. (5 points) Prove that every cauchy sequence is bounded below. an 2. (5 points) Let a sequence be defined by a1 = 1 an
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1. (5 points) Prove that every cauchy sequence is bounded below. an 2. (5 points) Let a sequence be defined by a1 = 1 an
1. (5 points) Prove that every cauchy sequence is bounded below. an 2. (5 points) Let a sequence be defined by a1 = 1 and an+1 - (2, +1) 1. Show that the sequence (an) converges. 2. Find the limit of the sequence 3. (5 points) Suppose (an) is a convergent sequence and (yn) is a sequence such that for any e > 0, there exists M such that for n M, we have an bile. Does it follow that (b) is convergent?
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