what does this sign mean???

[Guest]

It looks like the Greek epsilon? Or a m turned 1/4 back? I'm suppose to evalute tha sum...on the top line of it theres small (12) and at the bottom leg of it there's a (K=3) this looks to be multiplied by (1/2^k)?

I have 5 solution opptions
a. 1023/8
b. 1023/2048
c. 1/8
d. 1023/8192
e none of these

 

[tkhunny]

It's an upper case SIGMA - ∑ It indicates a sum of an expression, using a given index. In your case, the expression is 1/2^k, with 'k' as the index. Your task is to substitute ALL the values for k, defined as k = 3, k = 4, k = 5, ..., k = 12, and add up all 10 values.

So, what is 1/8 + 1/16 + 1/32 + 1/64 + ... + 1/4096?

Edit: Corrected. - Sorry about that.

 

[ChaoticLlama]

Close, but what you are reffering to is a capital Sigma.

And your question looks like...\(\displaystyle \sum\limits_3^{12} {\frac{1}{{2^k }}}\)

It means that you have the series defined by \(\displaystyle {\frac{1}{{2^k }}}\), and you need to add each element for the 10 values of k. k takes on the values 3,4,5,6,7,8,9,10,11,12.

 

[stapel]

I'm suppose to evalute tha sum.

Does this mean we're speaking to the student now, instead of the student's mother? If so, please reply showing what you have tried thus far. If this topic has not been covered in any of your classes (this would explain why you are not familiar with the notation or concepts), please state this, so we can try to find online lessons that can explain this topic to you.

Thank you.

Eliz.

 

[Guest]

yeah were both here

and we've tried adding the numbers to get 645 but do we add them as fractions or normal?? The 645 is just adding them up. fractions gave us 63/250?

these are bonus questions leadingup to the stuff there going to be starting in the lst 9 weeks??? But there's not much in her book about a few of these??? An and all help would be grreat. K and KD

 

[stapel]

Re: yeah were both here

and we've tried adding the numbers to get 645

Where is "645" coming from? Why are you attempting to obtain this value for the summation?

but do we add them as fractions or normal?

I'm sorry, but I don't know what this means. As has been explained, k takes on the values between 3 and 12, so the terms take on the values 1/2³, 1/2⁴, ... , 1/2¹². Since these are fractions, you would add these fractional terms. I'm afraid I'm not familiar with "fractional" versus "normal" addition...?

The 645 is just adding them up.

Adding what up? Please reply showing your steps and reasoning.

there's not much in her book...

So you're needing lessons on sigma notation, summations, and series...?

Thank you.

Eliz.

 

[Guest]

I finally got it I think!!!

I added 1/2^1-12 and came up with 1023/4096...which isn't one of the answers so I would have to answer E....is that what I should have come up with??? Thanks so much for answering and trying to help me no matter how slow we were....K and KD

 

[TchrQbic]

Re: I finally got it I think!!!

I added 1/2^1-12 and came up with 1023/4096...which isn't one of the answers so I would have to answer E....is that what I should have come up with??? Thanks so much for answering and trying to help me no matter how slow we were....K and KD

Yes, I believe that is correct . E is the answer here.

 

[Guest]

Thanks agai every body~~~ K

 

[stapel]

Re: I finally got it I think!!!

I added 1/2^1-12 and came up with 1023/4096...which isn't one of the answers

Where is "1/2¹ - 12" coming from?

As has been mentioned, the terms are of the form "1/2^k", with k going from 3 to 12, so the terms should look like 1/2³, 1/2⁴, ... , 1/2¹². Add those fractions.

Eliz.

 

[Mrspi]

Useful Formula.....

As has been pointed out by a number of previous posters, you are adding these fractions:

(1/8) + (1/16) + (1/32) + .... + (1/4096)

This is a geometric series, with first term 1/8, common ratio r = 1/2, and 10 terms.....(summing (1/2)<SUP>k</SUP> as k goes from 3 to 12 gives you 12 - 3 + 1 terms)

You can use this formula, which gives the sum of the first "n" terms of a geometric series with first term a<SUB>1</SUB> and common ratio r:

S<SUB>n</SUB> = (a<SUB>1</SUB> - a<SUB>1</SUB>*r<SUP>n</SUP>) / (1 - r)

For your problem, a<SUB>1</SUB> = 1/8, r = 1/2, and n = 10......