Question

I really need help fast.. Use summation notation to express the sum. 2- 1/2 + 1/8 -..... + 1/2048

Answer 1

seems to get divided by 2 every term

Answer 2

Can I just tell you if my answer is right? I have 7 over sigma, n=1 below the sigma. to the side I have (-8 times (-0.25)^n)

Answer 3

you tell me oops

Answer 4

and the sign alternates

Answer 5

what?

Answer 6

?

Answer 7

meanin +-+-

Answer 8

so mine is right?

Answer 9

The first term is 2. What are you dividing 2 by to get -1/2 ?

Answer 10

Oh you already have it, didn't see it. But your start at 2, not -8.

Answer 11

I have to go, can you just tell me if I am right please

Answer 12

Oh so is the side then: 2/4 ^n-1(-1)^n-1?

Answer 13

?????

Answer 14

one sec, I'm trying something out real quick

Answer 15

ok, then can u tell me if either of my choices are right?

Answer 16

isn't this a geometric series?

Answer 17

did u find out @jim_thompson5910

Answer 18

??????i need helppp

Answer 19

Notice how you start at 2

Your next term is -1/2

The common ratio is then


r = (term)/(previous term) = (-1/2)/2 = -1/4


So the geometric sequence is

an = 2*(-1/4)^(n-1)

Answer 20

Notice how when n = 7,


a7 = 2*(-1/4)^(7-1)

a7 = 1/2048

Answer 21

So @jim_thompson5910 , it would be n=7 on top of sigma, n=1 on bottom. and the side is an=-2/4^n-1??

Answer 22

would that be right?

Answer 23

This means that we stop at n = 7

So 2- 1/2 + 1/8 -..... + 1/2048 represented in summation notation is

\[\Large \sum_{n=1}^{7}2 \left( -\frac{1}{4} \right )^{n-1} \]

Answer 24

well that would be a geometric progression with r =-2\[u _{n}=u_{1} \times r ^{n-1}\]\[u _{1}=2\rightarrow u _{n}=2\times (-2) ^{n-1}\]\[\rightarrow u _{n}=(-1)^{n-1}\times2^{n}\]

Answer 25

So @jim_thompson5910 that sigma you have on the bottom is correct? u sure?

Answer 26

I agree but are u sure?

Answer 27

yes I'm sure

Answer 28

You can plug in arbitrary values of n to generate any term you want

Answer 29

and you should get a term that's in the given sequence above