SOLUTION: Expand the following sums: c) the summation from 2 to 5 of (-1)^i(x^(i-1))

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Question 1049687: Expand the following sums:
c) the summation from 2 to 5 of (-1)^i(x^(i-1))

Answer by ikleyn(52788) About Me  (Show Source):
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Expand the following sums:
c) the summation from 2 to 5 of (-1)^i(x^(i-1))
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1-st term:  i=2:   %28-1%29%5Ei%2Ax%5E%28i-1%29 = %28-1%29%5E2%2Ax%5E%282-1%29 = 1*x = x.


2-nd term:  i=3:   %28-1%29%5Ei%2Ax%5E%28i-1%29 = %28-1%29%5E3%2Ax%5E%283-1%29 = -1%2Ax%5E2 = -x%5E2.


3-rd term:  i=4:   %28-1%29%5Ei%2Ax%5E%28i-1%29 = %28-1%29%5E4%2Ax%5E%284-1%29 = 1%2Ax%5E3 = x%5E3.


4-th term:  i=5:   %28-1%29%5Ei%2Ax%5E%28i-1%29 = %28-1%29%5E5%2Ax%5E%285-1%29 = -1%2Ax%5E4 = -x%5E4.


Finally, the sum of these four terms is  x+-+x%5E2+%2B+x%5E3+-+x%5E4.