Question

Find the sum of the geometric series.

Answer 1

\[\sum_{k=1}^{100}2^-k\]

Answer 2

geometric series has common ratio,
can you find common ratio for this ?

Answer 3

is it 1/2?

Answer 4

absolutely correct! :)
1st term = a1 = 1/2
r =common ratio = 1/2
n = number of terms = 100
know the formula ?

Answer 5

yes I know the formula.. let me try it out.

Answer 6

this can come in handy :
http://openstudy.com/study#/updates/503bb2a0e4b007f9003103b0

Answer 7

how would I find -.5^12 using my calculator..?

Answer 8

I'm sorry .5^12?

Answer 9

you couls use google too...

Answer 10

yeah I would, but what if I get in a situation where I have just a calculator? let me show you my calculator...

Answer 11

.5^12 = (1/2)^12 = 1/ 2^12

Answer 12

and 2^12 = 4096

Answer 13

but why 12 ?

Answer 14

oops I might be doing this wrong.. . :/

Answer 15

n=100

S = (1/2) (1-(1/2)^100)/(1-1/2)

Answer 16

S= 1- (1/2)^100

Answer 17

how does n=100?

Answer 18

n = number of terms
since k goes fro m 1 to 100, number of terms = 100

Answer 19

omg... I'm really sorry, I wrote it wrong. sorry! let me write it ... hold on.

Answer 20

\[\sum_{k=1}^{12}2^-k\]

Answer 21

then n=12
S = 1-1/2^12

Answer 22

4095/4096

Answer 23

okay so n=12 , r=1/2, and t1= 1/2?

Answer 24

yes

Answer 25

what would be 1- 1/2^12 because I can't seem to calculate it right?

Answer 26

2^12 is 4096
so
1/2^12 = 1/4096

1-1/2^12 = 1-1/4096 = (4096-1)/4096 = 4095/4096

Answer 27

okay I get it now... that was a little tricky... thank you for helping.

Answer 28

welcome ^_^