SOLUTION: Write each series in summation notation. -2 + 4 - 8 + 16 - 32

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Question 872011: Write each series in summation notation.
-2 + 4 - 8 + 16 - 32
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
You recognize them as the first 5 powers of 2 with alternating signs,

which is the same as the first 5 powers of -2, that is,

(-2)1 + (-2)2 + (-2)3 + (-2)4 + (-2)5 

You can choose any letter as an "index" or "dummy variable", I'll
choose the letter k, but you can choose any letter:

sum%28%28-2%29%5Ek%2Ck=1%2Cmatrix%281%2C3%2C%22%22%2C%22%22%2C5%29%29

Very often when the signs alternate, a factor of (-1)k is preferred.
In that case you would write (-2)k as (-1)k2k, and write the summation as:

sum%28%28-1%29%5Ek%2A2%5Ek%2Ck=1%2Cmatrix%281%2C3%2C%22%22%2C%22%22%2C5%29%29

Edwin