Question

Help me find the sum please!

1 - 1/2 + 1/4 - 1/8 + ... -1/512

Answer 1

\(\sum_{n=0}^9(\frac{-1}{2})^n\)

Answer 2

yes I keep getting 0.666 (basically 2/3) and it's saying my answer is incorrect.

Answer 3

(1-1/2)+(1/4-1/8)+(1/16-1/32)...
1/2+1/8+1/32....+1/512
for 6 terms of a geometric progression apply formula

Answer 4

right that whole thing works for when we go to infinity, this has finite terms...

Answer 5

Is it an infinite GP?

Answer 6

I just noticed that it didnt have ..... at the end.

Answer 7

yeah it ends at -1/512

Answer 8

I believe there are 10 terms.

Answer 9

then first term is 1 and the common difference is -1/2
S = 1* (1-(-1/2)^10)/(1-(-1/2))

Answer 10

yes and I get 0.666 but it says my answer is incorrect, maybe the hw is incorrect

Answer 11

1023/1536

Answer 12

wait yeah its 1023/1536!

Answer 13

@aviz how did you get to that answer?

Answer 14

512 = 2^9 so the progression is 1 + (-1/2) + (-1/2)^2... +(-1/2)^9
So there are 10 terms
Formula for sum of finite GP = a (1-r^n)/(1-r)
a= first term, here 1
r= common ratio = -1/2
n =number of terms 10

S= 1*(1-(-1/2)^10)/(1-(-1/2)) = (1-(1/1024))/(1+1/2) = 1023/1536

Answer 15

@shamim - I think it is (1-r^n) not (1-r)^n in the numerator

Answer 16

ok

Answer 17

when it will b r^n-1
@aviz