1. (a) Let an→ 2. Prove from first principles (i.e. give a direct e-N proof) that a → 4. (b) Let an → 4. Prove that (an) has a subsequence which converges either to 2 or -2. (c) Let a →→ 4. Prove from first principles (i.e. give a direct e-N proof) that |an| → 2.

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Q: 1. (a) Let an → 2. Prove from first principles (i.e. give a direct e-N proof) that a → 4. (b) Let a?…

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A: Please see the below picture for detailed solution.

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A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…