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JH
Numerade Educator

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Problem 62 Medium 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 = \frac { 1 \cdot 3 \cdot 5 \cdot \cdot \cdot \cdot \cdot (2n - 1)}{n!} $

Answer

divergent

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Video Transcript

Let's use a graph of the sequence to decide whether converges or die rouges. So here, let's use this formula to find some of the ends. So here, for example, when we plug in and equals one, we just multiply up, too. Just one itself, divided by one factorial equals one. Now a two that's one times two times two minus one over to factorial. So three halfs and then a three similarly fifteen over six. So it's a little bigger than two a. Four. This is one oh, five over twenty four. Now that's a little bigger than four. So not only assisting increasing, but it seems the rate at which it's increasing is increasing, and one leads to another term here, a five that's nine forty five over one hundred twenty. A rough estimate of this more or less his nine Less than that, maybe eight would be closer. So definitely much bigger than before. So a little bigger than here around, eh? So we could see that this thing is just increasing, and this is just diversion is growing too fast. So from the graph we decide that it's diversion, and because of that, there's no more works show. So you want a little more insight here. You could not only is a diversion, you could even say the limit of Anna's infinity, and that's our final answer.