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Let an be a sequence that is bounded below by 0 and bounded above by 5

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Let an be a sequence that is bounded below by 0 and bounded above by 5. Further, assume that lim an = L for
some L E R. 7-+00 Using the formal definition of the limit of a sequence, show that lim 4(an - 2) = 4(L - 2). 1-00