1. ## Summation Help

I'm a little confused by summations and closed forms...

Can someone explain how the heck this works...
$\sum_{i=1}^{n}n-i+2$

By re-arranging the terms, this becomes:

$\sum_{i=1}^{n}i+1$

2. $\sum_{i=1}^n(n-i+2)=(n+1)+n+(n-1)+\ldots+2=$

$=2+3+\ldots+n+(n+1)=\sum_{i=1}^n(i+1)$

3. Originally Posted by red_dog
$\sum_{i=1}^n(n-i+2)=(n+1)+n+(n-1)+\ldots+2=$

$=2+3+\ldots+n+(n+1)=\sum_{i=1}^n(i+1)$
Maybe I'm just having a brain fade, but how did you get from (n+1)+n+(n-1).... to 2+3+...n+(n+1) to the final given summation.

4. You just have to look at it and see.

The first term of the new summation is i=1, i+1=1+1=2

i=2, i+1=2+1=3
.....
i=n, i+1=n+1

Pretty much you just have to write out the terms and see how it goes.

5. I hate to say this, but I'm still not following. It would be great if someone could step through it for me..

6. Check this out, hopefully you can apply the same logic to your problem:

Summations

7. Originally Posted by zhupolongjoe
Check this out, hopefully you can apply the same logic to your problem:

Summations
Thanks for the link but I already understand the basics of Summation. I'm sure this may come as a shock to some of you..

My confusion is how does (n+1) become 2, and then n becomes 3...

How does n + (n -1) become n + (n + 1)

8. Originally Posted by Twenty80
Thanks for the link but I already understand the basics of Summation. I'm sure this may come as a shock to some of you..

My confusion is how does (n+1) become 2, and then n becomes 3...

How does n + (n -1) become n + (n + 1)
Originally Posted by red_dog
$\sum_{i=1}^n (n-i+2) = (n+1)+n+(n-1)+\ldots+2=$
I assume you can see where each term comes from. Substitute i = 1, 2, 3, .....

Originally Posted by red_dog
$=2+3+\ldots+n+(n+1)=\sum_{i=1}^n(i+1)$
This is just the above written backwards. The summand on the right hand side should be obvious.

9. I see what confuses you. (n+1) does not "become" 2 and n does not
"become" 3. 2+3+....(n-2)+(n-1)+(n)+(n+1) is exactly the same as (n+1)+(n)+(n-1)+(n-2)+....+3+2...just backwards. Do you see it now?

10. haha, that's sad. You guys were right, I didn't realize it was the same thing but backwards.