Summation Notation Help

**AndrewP** · March 15th 2013, 09:08 PM

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!

**Prove It** · March 15th 2013, 09:15 PM

The sigma notation $\displaystyle \sum_{i = 1}^N { \left( X_i - \bar{X} \right)}$ gives us a shorthand for a sum with a counter i going from 1 to N, so it translates to $\displaystyle \left( X_1 - \bar{X} \right) + \left( X_2 + \bar{X} \right) + \left( X_3 + \bar{X} \right) + \dots + \left( X_N + \bar{X} \right)$ .

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

**AndrewP** · March 15th 2013, 09:50 PM

Originally Posted by Prove It

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

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.

**AndrewP** · March 16th 2013, 04:27 AM

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