# Summation Notation Help

• Mar 15th 2013, 09:08 PM
AndrewP
Summation Notation Help
Hey guys!

I have no idea about this stuff and haven't really seen it before, any help is appreciated because I'm really struggling; thanks!

http://i46.tinypic.com/212ftc3.png
• Mar 15th 2013, 09:15 PM
Prove It
Re: Summation Notation Help
The sigma notation $\displaystyle \displaystyle \sum_{i = 1}^N { \left( X_i - \bar{X} \right)}$ gives us a shorthand for a sum with a counter i going from 1 to N, so it translates to $\displaystyle \displaystyle \left( X_1 - \bar{X} \right) + \left( X_2 + \bar{X} \right) + \left( X_3 + \bar{X} \right) + \dots + \left( X_N + \bar{X} \right)$.

Similarly, the pi notation $\displaystyle \displaystyle \prod _{j = 0}^{x-1} {\left( x - j \right) }$ gives us a shorthand for a product with a counter j going from 0 to x - 1. So it translates to $\displaystyle \displaystyle \left( x - 0 \right) \left( x - 1 \right) \left( x - 2 \right) \dots \left[ x - \left( x - 1 \right) \right] = x \left( x - 1 \right) \left( x - 2 \right) \dots 1$.
• Mar 15th 2013, 09:50 PM
AndrewP
Re: Summation Notation Help
Quote:

Originally Posted by Prove It
Similarly, the pi notation $\displaystyle \displaystyle \prod _{j = 0}^{x-1} {\left( x - j \right) }$ gives us a shorthand for a product with a counter j going from 0 to x - 1. So it translates to $\displaystyle \displaystyle \left( x - 0 \right) \left( x - 1 \right) \left( x - 2 \right) \dots \left[ x - \left( x - 1 \right) \right] = x \left( x - 1 \right) \left( x - 2 \right) \dots 1$.

What are you getting at with this?

I understand you explanation of part (a), (thank you so much!), but I don't really understand how this helps me out.
• Mar 16th 2013, 04:27 AM
AndrewP
Re: Summation Notation Help
bump