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Compute the sum of the geometric series -1+2-4+8...+512.

Guest Oct 2, 2017
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 #1
avatar+79786 
+1

We can split this into  two series

 

2 + 8 + 32 +  128  + 512      and     -1 + -4 + - 16 + - 64 + -256  = - [ 1 + 4 + 16 + 64+ 256 ]

 

 

Note that the first series can be written as

 

2 [ 1 + 4 + 16 + 64+ 256 ] 

 

So the sum of the two series  is

 

2 [A]  - [A]       =   A   

 

Where A  is just  1 + 4 + 16 + 64+ 256   =  341 !!!

 

 

cool cool cool

CPhill  Oct 2, 2017
 #2
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+1

Sum =F x [1 - R^N] / [1 - R], where F=First term, R=Common ratio, N=Number of terms

Sum =-1 x [1 - (-2^10] / [1 - (-2)]

Sum =-1 x [1 - 1,024] / [3]

Sum =-1 x[ -1023] / 3

Sum = 1,023/3

Sum = 341

Guest Oct 2, 2017

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