SOLUTION: use summation notation to write the series: 1- 1/2+ 1/4- 1/8+ ...- 1/128

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Question 347947: use summation notation to write the series: 1- 1/2+ 1/4- 1/8+ ...- 1/128
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
note a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29where a%5B1%5D is the first term and n the common ratio. In this series the common ratio is r = -(1/2)
.
knowing the value of the nth term: find the number of terms in the series
%28-1%2F128%29=+%28-1%2F2%29%5B1%5D%2Ar%5E%28n-1%29
%28-1%2F128%29=+%28-1%2F2%29%2Ar%5E%28n-1%29
%281%2F64%29=+%28-1%2F2%29%5E%28n-1%29
%28-1%2F2%29%5E6=+%28-1%2F2%29%5E%28n-1%29
6 = n-1
7 =n
.
finding the sum of the terms can be found by the following
S%5Bn%5D+=+a%5B1%5D%281-r%5En%29%2F%281-r%29
substitute:
sum%28%282%2F3%29%281-r%5En%29%2C+n=1%2C+7+%29