# Thread: Writing the Sum Using Sigma Notation

1. ## Writing the Sum Using Sigma Notation

Alright, it goes hand-in-hand with a previous topic titled "Summation Formulas" but yet...it's different at the same time.

This time they give me two series:

1. $1+1/2+2+5/2+...+6$

2. $[1-(1/2)^2]+[1-(1/3)^2]+[1-(1/4)^2]+...$

My first reaction was that I would have to find the formula myself, where it starts, and where it ends. Simple...except not so much.

The second one is possibly $\sum_{n=1}^{INF}([1-(1/(1+N)^2])$.

Although that would be way to simple, hehe.
The first one though, I can't seem to find a proper equation that fits the numbers given.

2. ## Re: Writing the Sum Using Sigma Notation

The answer to the second one is correct.

You could even say $\displaystyle \sum_{n=2}^{\infty}1-\frac{1}{n^2}$

Can't see a pattern in the first one yet.

3. ## Re: Writing the Sum Using Sigma Notation

Yeah, I dunno what's going on with the first one. I spent at least an hour or two going over it but it's harder then it looks...and it looked pretty hard to start with.

Oh, I also made a mistake on number one, accidently left out a number. Fixed it.

Should be:

$1+\frac{1}{2}+2+\frac{5}{2}+...+6$

4. ## Re: Writing the Sum Using Sigma Notation

Originally Posted by UnstoppableBeast
Alright, it goes hand-in-hand with a previous topic titled "Summation Formulas" but yet...it's different at the same time.

1. $1+{\color{red}1}/2+2+5/2+...+6$
I think it ought to be $1+\frac{{\color{blue}3}}{2}+2+\frac{5}{2}+\cdots+6$.

In which case it would be $\sum\limits_{k =1}^{11} {\frac{{k + 1}}{2}}$

5. ## Re: Writing the Sum Using Sigma Notation

Is it possible the second term has to be $\frac{3}{2}$ in stead of $\frac{1}{2}$?

6. ## Re: Writing the Sum Using Sigma Notation

Sadly no. It would've been easier that way but I'm sure of what the question is asking, I have the paper right in front of me.

Maybe the person who made the packet made a mistake, seems as likely as anything.