Find the sum of the geometric series

Question

32-8+2-1/2+....

a) 128/9   c) 128/5

b) 256/5    D) 128/3

Answer 1

Dhelmalyz,

 

I'd like to point out an alternative way to look at this:

 

32,-8,+2,-1/2+....

 

is in fact the difference of two geometric series with the same positive ratio, 1/16:

 

32,2,1/8

 

8,1/2.1/32

 

So S=  (32-8)/(1-1/16)=24*16/15=128/5

 

Answer 2

Formula for sum of geometric series:

 

Sum = a/(1-r)

 

where a is the first term and r is what we multiply by each time.

 

a = 32

 

To find r: -8/32 = -1/4; 2/-8 = -1/4.  So r = -1/4

 

Sum = 32/(1-(-1/4)) = 32/(1+1/4) = 32/(5/4) = 32*4/5 = 128/5

Answer 3

Hi Dhelmalyz,

 

32-8+2-1/2.......

 

Sum of infinite Geometric series= a/1-r

 

a= 32, r= -1/4

 

sum of Geometic series= 32/1-(-1/4)

                                  =32/5/4 

                                   =128 /5