Thread: confused! geometric sum

determine the sum of the following geometrec sereis.

-1/32+ 1/16...........+ 256

well I know that I would use the formula:
sn=a (1-r^n)/1-r

a=-1/32
r=
n=

okay this were I get lost can you expalin to me what I nedd to do next? thanks for your help!

Originally Posted by frogsrcool

determine the sum of the following geometrec sereis.
-1/32+ 1/16...........+ 256
well I know that I would use the formula:
sn=a (1-r^n)/1-r
a=-1/32
r=
n=
...

Hi,

are you certain that your serie starts with -1/32? (I presume that this is a typo:

1/32+ 1/16...........+ 256 = 2^(-5)(1 + 2 + 4 + ...+2^13)
So:
a=1/32
r=2
n=13

thus s_13 = 16383/32 nearly 512

EB

Originally Posted by earboth

Hi,

are you certain that your serie starts with -1/32? (I presume that this is a typo:

The common ratio could be -2, the number of terms is right for the sign
of 256 to be +:

-1/32, 1/16, -1/8, 1/4, -1/2, 1, -2, 4, -8, 16, -32, 64, -128, 256

RonL

Hi,

OK, with CaptBlack's answer I understand your problem:

Your serie is: -1/32, 1/16, -1/8, 1/4, -1/2, 1, -2, 4, -8, 16, -32, 64, -128, 256

To get the result there are two different ways:

1) Put together two summands:
-1/32 + 1/16 = 1/32
-1/8 + ¼ = 1/8
-1/2 + 1 = ½
...
you get a final serie: 1/32, 1/8, 1/2, 2, 8, 32, 128
(for confirmation only: 170.65625 = 5461/32)

2) Split your serie into two series. The first one contains all negative summands, the second one the positive summands. Calculate the sums separately. Add the sums (be aware that one sum is negative!)
(for confirmation only: -170.65625 + 341.3125 = 170.65625)

EB

hey I used the formula and it worked out so thanks alot! I understand what I am doing! I am very grateful!