Consider the sequence (an)n-1 defined as follows: a = 4 and an = = 4 -...

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Consider the sequence (an)n-1 defined as follows: a₁ = 4 and an = = 4 - 3 an-1 for all n ≥ 2. (1) Use mathematical induction to prove that 2 ≤ an ≤ 4 for all n ≥ 1. (2) Use mathematical induction to prove that (an) is a decreasing sequence. (3) is the sequence (an)1 convergent? Explain. If it is convergent, find its limit. Consider the sequence (an)n-1 defined as follows: a₁ = 4 and an = = 4 - 3 an-1 for all n ≥ 2. (1) Use mathematical induction to prove that 2 ≤ an ≤ 4 for all n ≥ 1. (2) Use mathematical induction to prove that (an) is a decreasing sequence. (3) is the sequence (an)1 convergent? Explain. If it is convergent, find its limit.

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