In Exercises 1–6, write the first four terms of each sequence who...

Question

In Exercises 1–6, write the first four terms of each sequence whose general term is given. a_n = 1/(n - 1)!

Accepted Answer

Hello. Today we're going to be finding the first four terms of this given sequence. So the sequence given to us is a sub n equal to four over n plus one factorial. So when we're looking for the first four terms what it means is that we're looking for a sub one, A sub two A sub three and four. And in each of these cases we're allowing N to equal the subscript. So for example if we're looking for a sub one we're allowing em to equal to one. So doing this, a sub one is going to equal to 4/1 plus one factorial. Now one plus one is going to be too. So what this gives us is 4/2 factorial and two factorial could be expanded as two times one and two times one is just gonna be too. So what this leaves us with is 4/2 which is equal to two. So a sub one is going to be equal to two. Now we're gonna go ahead and repeat this process for a sub two, a sub three and a sub four. So for a sub two and it's going to equal to two. So we have 4/2 plus one factorial. And what that gives us is 4/3 factorial. Now three factorial could be expanded as three times two times one which is going to equal to six. So what we're left with is 4/6 which simplifies to 2/3. So a sub two is going equal to two thirds. Alright now continuing this for a sub three and is going to equal to three. So that gives us 4/3 plus one factorial And this is gonna give us 4/4 factorial. Four factorial expands as four times three factorial. Now the reason why I left it like this is because we can go ahead and cancel of four in both the numerator and denominator and we know that from a sub 23 factorial is equal to six, so this simplifies to 1/6. So a sub three is going to equal to 1/ and finally for a sub four and is equal to four. So we have 4/4 plus one factorial And that's going to simplify to 4/5 factorial. Now five factorial could be written now as five times four times three times two times one, which is going to simplify to four over which will simplify to 1/30. So a sub four is going to equal to 1/ and this is going to be the first four terms of this sequence. That also means that the answer to this problem is going to be be So I hope this video helps you in understanding how to find the terms of a sequence and I'll go ahead and see you all in the next video

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In Exercises 1–6, write the first four terms of each sequence whose general term is given. a_n = 1/(n - 1)!

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