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

 

40−10+2.5−0.625+...

 Jan 11, 2020
 #1
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We have  a geometric series  where  the common ratio, r , =  -1/4

 

The sum of the  first six terms is given  by

 

first term *  [ 1 - r^6 ] / [ 1 - r ] = 

 

40  [ 1 - (-1/4)^6 ] /  [ 1 - - 1/4]  =

 

40  [ 1 - ( 1/4096)]  / [ 5/4]  =

 

(4 * 40) [ 4096 - 1] / [ 5 * 4096 ]  =

 

160 *  4095  / [ 20480 ] = 

 

655200 / 20840   =

 

4095 / 128

 

 

cool cool cool

 Jan 11, 2020

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