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Does the sequence {a_n} converge or diverge? Find the limit if the sequence is convergent. a_n=[(n+4)/5n][1-(4/n)]
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One way to do this is to simplify the expression. a_n = (n+4)/(5n) - (4n + 16)/(5n^2) = 1/5 + 4/(5n) - 4/(5n) - 16/(5n^2) = 1/5 - 16/(5n^2) So a_n = 1/5 - 16/(5n^2). So as n goes to infinity, we see a_n approaches 1/5.
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