Join TSR now and get all your revision questions answeredSign up now

using the summation operator- a small doubt Watch

    • Thread Starter
    Offline

    0
    ReputationRep:
    Name:  sts.jpg
Views: 48
Size:  16.7 KB

    How does the 1st line (of the summation operator) become the 2nd one?
    Offline

    2
    ReputationRep:
    You are asking why n\left(\sum_i x_i^2 + \sum_i x_i^2\right) = n \sum_i 2x_i^2...

    ...because x_i^2+x_i^2 = 2x_i^2 for each i and multiplication distributes over addition. There isn't really any way to break it down other than what they wrote unless you want to start defining addition and multiplication of plain numbers.

    Quit using stupid terms like summation operator and just remember that you are dealing with a simple sum of terms.

    Write \sum_{i=1}^n x_i^2 = x_1^2 + x_2^2 + \cdots + x_n^2 if it helps.
    • Community Assistant
    Offline

    19
    ReputationRep:
    (Original post by Mark85)
    Quit using stupid terms like summation operator
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by Mark85)
    You are asking why n\left(\sum_i x_i^2 + \sum_i x_i^2\right) = n \sum_i 2x_i^2...

    ...because x_i^2+x_i^2 = 2x_i^2 for each i and multiplication distributes over addition. There isn't really any way to break it down other than what they wrote unless you want to start defining addition and multiplication of plain numbers.

    Quit using stupid terms like summation operator and just remember that you are dealing with a simple sum of terms.

    Write \sum_{i=1}^n x_i^2 = x_1^2 + x_2^2 + \cdots + x_n^2 if it helps.
    Posted the wrong question, sorry. I meant I don't get the last line-- how the final result is obtained from the penultimate.
    Offline

    3
    ReputationRep:
    (Original post by zomgleh)
    Posted the wrong question, sorry. I meant I don't get the last line-- how the final result is obtained from the penultimate.
    \frac{1}{n}\sum\limits_{i=1}^n x_i=\bar{x}
    Sub this in. It is similar to the proof of equivalence of 2 forms of the standard deviation formula.
    Offline

    2
    ReputationRep:
    Well, the mean is just

    \frac{1}{n}\sum_{i=1}^n x_i

    so

    \sum_i x^2_i - n\overline{x}^2 = \sum_i x^2_i - \left(\sum_i x_i\right)^2

    Can you see what to do from there? Have you even tried anything? The bit you quoted mentions a 'trick' - it isn't a trick in any sense, just a standard rearrangement but in any case, the reference to it suggests you will have seen it subsequently in the notes or books or whatever it is.

    If you prefer, write it out without the 'summation operator' as you grandiosely style it or even just write it out explicitly for n=3 or something so you see it.
 
 
 
Poll
If you won £30,000, which of these would you spend it on?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Quick reply
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.