47-53 Use a graph of the sequence to decide whether the sequence is convergent or divergent. If the sequence is convergent, guess the value of the limit from the graph and then prove your guess. (See the margin note on page 680 for advice on graphing sequences.) 47. $a_n = 1 + (-2/e)^n$ 48. $a_n = \sqrt{n} \sin(\pi/\sqrt{n})$
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Step 1: The sequence $a_n = 1 + (-2/e)^n$ is convergent. Show more…
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Use a graph of the sequence to decide whether the sequence is convergent or divergent. If the sequence is convergent, guess the value of the limit from the graph and then prove your guess. $$ a_{n}=1+(-2 / e)^{n} $$
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$57-63$ Use a graph of the sequence to decide whether the sequence is convergent or divergent. If the sequence is convergent, guess the value of the limit from the graph and then prove your guess. (See the margin note on page 695 for advice on graphing sequences.) $$a_{n}=\sqrt{n} \sin (\pi / \sqrt{n})$$
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Use a graph of the sequence to decide whether the sequence is convergent or divergent. If the sequence is convergent, guess the value of the limit from the graph and then prove your guess. (See the margin note on page 680 for advice on graphing sequences.) $$ a_{n}=1+(-2 / e)^{n} $$
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