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What is the sum of the first six terms of the series?

32−8+2−0.5+...

Enter your answer as a simplified fraction in the box. 

 Jan 27, 2021
 #1
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Every successive term  is   -(1/4)  * previous term  = r

 

The sum  is

 

first term  ( 1 -  r^6)  /( 1 - r)  =

 

32  ( 1 - (-1/4)^6)  / (1 -  - 1/4)  =

 

32  ( 1 - (-1/4)^6)  / ( 5/4)  =

 

32  ( 4/5)  ( 1 - (-1/4)^6)  =

 

128  /5  *  ( 1 - (-1/4)^6 )  =

 

819 / 32

 

 

 

cool cool cool

 Jan 27, 2021

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