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Numerade Educator

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Problem 7 Easy Difficulty

List the first five terms of the sequence.
$ a_n = \frac {1}{n + 1}! $

Answer

$\left\{\frac{1}{2}, \frac{1}{6}, \frac{1}{24}, \frac{1}{120}, \frac{1}{720}, \dots\right\}$

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Video Transcript

Okay, so this should be written one over in plus one factorial, we're taking the factorial of n plus one, not taking the factorial of some fraction Mhm. Okay, so for an equals one, we have 1/2 factorial two factorial is just too. That's just one half. So you just need to remember that in factorial is equal to end times in minus one times in minus two all the way down two times one. Okay, so now we have for n equals two went over in plus one factorial. So that's 1/3 factorial. So three factorial is three times two, which is six for n equals three. We have one over four Factorial. Another way that we can do this is four Factorial is the same thing as four times three factorial. So four times six gives us 24. So that's just a shortcut you can use. So for in equals four, we have 1/5 factorial and again, five factorial is the same thing as five times four factorial. So five times 24 is on 20 for n equals five it's 1/6 factorial six factorial is six times five factorial. Hi. Effect. Oil is 1 20. So we get 1/1 70 here, so that gives us the first five terms in our sequence here.