1. Summation Notation question help

Hi

I have this practice question but I have no idea how to approach.
Any help guiding me on the theory of how to do this question is appreciated.

Thanks

2. Re: Summation Notation question help

Just in case a picture helps...

_________________________________________

Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote!

3. Re: Summation Notation question help

For part (a):
You're given:
$\overline{X}=n^{-1}\sum_{i=1}^{n}X_i$ (expression (1)) and you need to prove that: $\sum_{i=1}^{n}(X_i-\overline{X})=0$ (expression (2))
Substitute (1) in (2):
$\sum_{i=1}^{n} \left(X_i-n^{-1}\sum_{i=1}^{n}X_i\right)$
To see clearly what happens we write down a few terms of the summation:
$[X_1-n^{-1}(X_1+X_2+\ldots+X_n)]+[X_2-n^{-1}(X_1+X_2+\ldots+X_n)]+\ldots+[X_n-n^{-1}(X_1+X_2+\ldots+X_n)]$
this is equal to:
$(X_1+X_2+\ldots+X_n)-nn^{-1}(X_1+X_2+\ldots+X_n)=0$

4. Re: Summation Notation question help

Hi guys thanks for the help
Thankyou