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#26 2010-05-22 02:50:11

soroban
Member
Registered: 2007-03-09
Posts: 452

Re: Summation


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#27 2010-05-22 22:00:53

soha
Real Member
Registered: 2006-07-07
Posts: 2,530

Re: Summation

Why taking n(n+1) / 6 as common?????

I can see only half of the previous post.. How is it like that?

Last edited by soha (2010-05-22 22:01:40)


"Let us realize that: the privilege to work is a gift, the power to work is a blessing, the love of work is success!" smile smile
- David O. McKay

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#28 2010-05-22 22:05:12

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Summation

Hi soha;

Everybody answered the question, a case of too many cooks spoiling the broth.

This is what you have to sum from 1 to n:

Here the sums are done one at a time.

There are algebraic tricks to get some of these but they are just gimmicks. As I told you there is no way to explain the real way these sums are done, without the use of the summation calculus.  Which is beyond the integral calculus. If you haven't had these then you must know the definite sums of k, k^2 and k^3. Or use the tables I have provided in the next post.


You can see you can pull an n (n+1) from each term.

Now add up whats inside that big parentheses on the RHS:

So A) is:

This is the answer:

If you put n = 20 into that you will get 188 090.

If you have to do more of these I will provide you with a table of sums so you will have them for next time. Just ask.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#29 2010-05-22 22:58:44

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Summation

Here is a table of definite sums you can use in the future:

If you have covered integral calculus, then I will be glad to show you how to use the summation calculus and factorial powers to get all of those and many more. If not you will find this table handy in the future.

This page here has many sums also:

http://en.wikipedia.org/wiki/Summation


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#30 2010-05-22 23:14:56

soha
Real Member
Registered: 2006-07-07
Posts: 2,530

Re: Summation

I am getting confused ..

Another question now, I will come back to this question later.

The Question is: -

Find the sum of n terms of the series:-

I tried doing it this way :-



Am I going right?

Last edited by soha (2010-05-22 23:23:52)


"Let us realize that: the privilege to work is a gift, the power to work is a blessing, the love of work is success!" smile smile
- David O. McKay

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#31 2010-05-22 23:19:01

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Summation

Hi soha;

Relax, I'll help. I did the problem for you in post #28. It is okay to feel confused, happens to everybody. Take a look at my work and my tables underneath. Everyone has answered your question correctly but we all did it differently, so it is natural for you to be confused.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#32 2010-05-22 23:25:16

soha
Real Member
Registered: 2006-07-07
Posts: 2,530

Re: Summation

I have edited my previous post and completed it.
Please have a look at it.


"Let us realize that: the privilege to work is a gift, the power to work is a blessing, the love of work is success!" smile smile
- David O. McKay

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#33 2010-05-22 23:32:18

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Summation

Nope, you have made an error somewhere.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#34 2010-05-22 23:34:55

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Summation

You are right up to here with your calculations. Except your notation is not good. I will straighten that out later.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#35 2010-05-22 23:46:13

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Summation

Work your new problem like this:

Break it up into smaller parts. Parts you know how to do.



simplifying

do more:

And we are done:


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#36 2010-05-22 23:48:56

soha
Real Member
Registered: 2006-07-07
Posts: 2,530

Re: Summation

What kind of notation? ?

What wrong did i do in pulling that common out??

Actually , I did not get that step yet .


"Let us realize that: the privilege to work is a gift, the power to work is a blessing, the love of work is success!" smile smile
- David O. McKay

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#37 2010-05-22 23:55:30

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Summation

See post # 35: You are using indefinte sum when you need to use definite sum. Notation is everyhting here! I have explained this earlier in this thread. Please see what I have done. Also you are summing from 1 to n. Those are the indices, they go on top and bottom. You use another "dummy variable" in this case k, sometimes i. I prefer k.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#38 2010-05-23 00:03:38

soha
Real Member
Registered: 2006-07-07
Posts: 2,530

Re: Summation

indefinate sum?? And definate sum??? What is this??

We have something as summation of finite series.. I don't know whether it is indefinate or definate?


"Let us realize that: the privilege to work is a gift, the power to work is a blessing, the love of work is success!" smile smile
- David O. McKay

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#39 2010-05-23 00:08:56

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Summation

That is a definite sum like a definite integral, see the k=1 to n. This is an actual summing of quantities.

That is an indefinte sum like an indefintie integral. It is not exactly a sum of discrete quanties but rather the anti difference operator. There is the difference operator and its inverse the anti difference or indefinite sum operator. Just like calculus, only this is discrete. You don't have to understand this now. But when you were told to sum from 1 to n you know you are using definite summation (the top one)

When you are summing a finite series that is a definite summation ( the top one ) Even if it was an infinite series it would still be a definite sum. k would be counting from 1 to infinity, but still counting.

All that is jargon, forget it right now. Do you follow what I did in post # 35 ?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#40 2010-05-23 18:03:37

soha
Real Member
Registered: 2006-07-07
Posts: 2,530

Re: Summation

Why did you try to find the value of

in that?


"Let us realize that: the privilege to work is a gift, the power to work is a blessing, the love of work is success!" smile smile
- David O. McKay

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#41 2010-05-23 18:50:50

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Summation

Hi soha;

In what, I don't follow you?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#42 2010-05-23 20:58:24

soha
Real Member
Registered: 2006-07-07
Posts: 2,530

Re: Summation

bobbym wrote:

this one... Why did you find 2k^2 here?


"Let us realize that: the privilege to work is a gift, the power to work is a blessing, the love of work is success!" smile smile
- David O. McKay

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#43 2010-05-23 21:01:13

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Summation

Isn't that the sum you wanted done? The one I did in post #35?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#44 2010-05-24 00:12:15

ZHero
Real Member
Registered: 2008-06-08
Posts: 1,889

Re: Summation

soha wrote:

this one... Why did you find 2k^2 here?

Hope you got it!


If two or more thoughts intersect, there has to be a point!

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#45 2010-05-24 00:24:14

ZHero
Real Member
Registered: 2008-06-08
Posts: 1,889

Re: Summation

soroban wrote:



wave    sad         up       swear        lol         dizzy          wink


If two or more thoughts intersect, there has to be a point!

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#46 2010-05-24 01:23:00

soha
Real Member
Registered: 2006-07-07
Posts: 2,530

Re: Summation

I understood this whole lot somehow but... I am struck still.

I get the value of tn.. Using that table, i get the values of n^2 , n^3 or what ever....
but then bringing out  the common???? I am struck at this point in each and every problem.....

I think I can never do this.


"Let us realize that: the privilege to work is a gift, the power to work is a blessing, the love of work is success!" smile smile
- David O. McKay

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#47 2010-05-24 01:39:52

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Summation

Hi soha;

Where are you stuck exactly? Post # 35 does the whole thing for you.

or


You can see that you can pull out an n (n+1) from each term:


Clean up the bunch inside the big parentheses on the RHS:


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#48 2010-05-31 00:06:42

soha
Real Member
Registered: 2006-07-07
Posts: 2,530

Re: Summation

I still din't get how we pull something??

I mean how to decide which one must be taken out as common?


"Let us realize that: the privilege to work is a gift, the power to work is a blessing, the love of work is success!" smile smile
- David O. McKay

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#49 2010-05-31 00:08:41

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Summation

Hi soha;

It takes some experience before you can see how to pull out factors. It is not even really necessary. A) is correct too. Just not simplified. If you have a few examples I will be glad to go over them with you, if I can.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#50 2010-05-31 00:19:15

soha
Real Member
Registered: 2006-07-07
Posts: 2,530

Re: Summation

So the only way I learn it is by doing a lot of problems of this kind.


"Let us realize that: the privilege to work is a gift, the power to work is a blessing, the love of work is success!" smile smile
- David O. McKay

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