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JH
Numerade Educator

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Problem 57 Easy Difficulty

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 699 for advice on graphing sequence .)
$ a_n = (-1)^n \frac {n}{n + 1} $

Answer

diverges.

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Video Transcript

Let's use the graph of the sequence to decide whether a convergence or die virgins. So here's a formula for our sequence. Let's go to decimals. Graphing calculator to graph our sequence. Here we can graft, let's say, seventy terms and here's the graph of our sequence. We can see an absolute value. It's getting closer. One, however it is alternating. So based on the graph, it looks like the Siri's should diverge. Our excuse me, the sequence. So basically what's happening here is we know that the limit his N goes to infinity of end over end plus one equals one. So that's this part right? Here goes toe one. However, we still have this negative one outside. So this means that is Angus Large A N is oscillating between negative one one. So does not converge. And that's our final answer