SOLUTION: The first 4 terms of the following sequence an= (-2)^n/(n!) are -2,2,-4/3,2/3 True or False

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Question 1082979: The first 4 terms of the following sequence an= (-2)^n/(n!) are -2,2,-4/3,2/3
True or False
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

a%5Bn%5D=+%28-2%29%5En%2F%28n%21%29

Let's plug in 1 for n and see if we get -2 for the 1st term.

a%5B1%5D=+%28-2%29%5E1%2F%281%21%29
a%5B1%5D=+%28-2%29%2F1
a%5B1%5D=+-2

So the 1st term is -2.  So far so good.

Now, let's plug in 2 for n and see if we get 2 for the 2nd term.

a%5B2%5D=+%28-2%29%5E2%2F%282%21%29
a%5B1%5D=+4%2F%282%2A1%29
a%5B1%5D=+4%2F2
a%5B2%5D=2

So the 2nd term is 2.  So far so good.

Now, let's plug in 3 for n and see if we get -4/3 for the 3rd term

a%5B3%5D=+%28-2%29%5E3%2F%283%21%29
a%5B3%5D=+%28-8%29%2F%283%2A2%2A1%29
a%5B3%5D=+%28-8%29%2F6
a%5B3%5D=+-8%2F6
a%5B3%5D=-4%2F3

So the 3rd term is -4/3.  So far so good.

Finally, let's plug in 4 for n and see if we get 2/3 for the 4th term.

a%5B3%5D=+%28-2%29%5E4%2F%284%21%29
a%5B3%5D=+16%2F%284%2A3%2A2%2A1%29
a%5B3%5D=+16%2F24
a%5B3%5D=+2%2F3

Yep!  So that proves that the answer is "TRUE".

Edwin