The question:Rewriting Series with Sigma Notation

[Mo]

Series and "Sigma" Notation

I have been revising over the sigma/sequences and series chapters, this is the second question now where i have had different answers to the book - yet- my answers seem to work - i think...

The question :

Write in $$\sum$$ notation

1 - 2 + 4 - 8 + 16 - 32


My answer is:

$$\sum_{0}^5 -2^r$$

Is this correct?

Thie answer in the book by the way is:

$$\sum_{1}^6 (-1)^{r+1} \ 2r^{r-1}$$

Regards,
Mo

 

[Muzza]

I have been revising over the sigma/sequences and series chapters, this is the second question now where i have had different answers to the book - yet- my answers seem to work - i think...

The question :

Write in $$\sum$$ notation

1 - 2 + 4 - 8 + 16 - 32


My answer is:

$$\sum_{0}^5 -2^r$$

Is this correct?
...

Nope. Every term in that sum is negative (which is not true for 1 - 2 + 4...).

 

[dextercioby]

Then the answer in the books seems wrong and yours as well.
$$1-2+4-8+16-32=(-)^{0}2^{0}+(-)^{1}2^{1}+(-)^{2}2^{2}+(-)^{3}2^{3}+(-)^{4}2^{4}+(-)^{5}2^{5}=\sum_{k=0}^{5}(-)^{k}2^{k}$$

You might have mistyped the answer in the book.

Daniel.

 

[Mo]

Yes i have typed in ther answer from the book wrongly, very sorry about that.

$$\sum_{1}^6 (-1)^{r+1} \ 2^{r-1}$$

is the correct one.

However i still can't see how my answer is wrong!

when r is 0 , the answer is +1
when r is 1 , the answer is -2
when r is 2 , the answer is +4
when r is 3 , the answer is -8

so this would mean +1-2+4-8 ? Or maybe I am making a really stupid mistake here!

Thanks for your replies so far!

 

[Nylex]

However i still can't see how my answer is wrong!

when r is 0 , the answer is +1
when r is 1 , the answer is -2
when r is 2 , the answer is +4
when r is 3 , the answer is -8

so this would mean +1-2+4-8 ? Or maybe I am making a really stupid mistake here!

Thanks for your replies so far!

At first, I thought your answer was right. It's not, cos your sum is -2^r and not (-2)^r. When r is 0, for your answer, you get -1, ie. -1 x 2^0.

 

[Zaimeen]

Your answer would have been correct if you would have used this one: -

The following code was used to generate this LaTeX image:



$$\sum_{k=0}^{5}(-2)^{k}$$

 

[jtbell]

Look at it this way: If you had

$$\sum (1-2^r)$$

would you say that was

$$(1-1) + (1-2) + (1-4) + ...$$

or

$$(1+1) + (1-2) + (1+4) + ...$$

?

When you evaluate an expression that doesn't have parentheses inside of it, and is on a single line, exponents always come first, then multiplication/division, then addition/subtraction.

 

[Mo]

Thank you for your replies all

Offcourse i should have used brackets :sigh: next time ill remember!

thanks again

Regards,
Mo

PS: JTbell, this first one ..

 

[jtbell]

I just realized that I got the signs backwards on my second choice.

Oh well, you got the right idea, anyway!