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What is the sum of the first 7 terms of the series  −8+16−32+64−... ?

 Mar 21, 2019
 #1
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We have a geometric series.....the common ratio   is    16/ - 8  = -2

 

The sum of the first n terms is given by:

 

first term  [  1 -  common ratio^n  ] / [ 1  - common ratio ]         

 

So.....the  sum is

 

-8 [ 1 - (-2)^(7) ] / [ 1 - (-2) ]  =

 

-8 [  1  -  (-2)^7]  / [ 3 ]   =  

 

-8 (129) / 3  =

 

-8 ( 43)  =

 

-344

 

 

cool cool cool

 Mar 21, 2019

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