Summation

soroban · 2010-05-22 02:50:11

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soha · 2010-05-22 22:00:53

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)

bobbym · 2010-05-22 22:05:12

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.

bobbym · 2010-05-22 22:58:44

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

soha · 2010-05-22 23:14:56

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)

bobbym · 2010-05-22 23:19:01

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.

soha · 2010-05-22 23:25:16

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

bobbym · 2010-05-22 23:32:18

Nope, you have made an error somewhere.

bobbym · 2010-05-22 23:34:55

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

bobbym · 2010-05-22 23:46:13

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:

soha · 2010-05-22 23:48:56

What kind of notation? ?

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

Actually , I did not get that step yet .

bobbym · 2010-05-22 23:55:30

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.

soha · 2010-05-23 00:03:38

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?

bobbym · 2010-05-23 00:08:56

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 ?

soha · 2010-05-23 18:03:37

Why did you try to find the value of

in that?

bobbym · 2010-05-23 18:50:50

Hi soha;

In what, I don't follow you?

soha · 2010-05-23 20:58:24

bobbym wrote:

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

bobbym · 2010-05-23 21:01:13

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

ZHero · 2010-05-24 00:12:15

soha wrote:

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

Hope you got it!

ZHero · 2010-05-24 00:24:14

soroban wrote:

soha · 2010-05-24 01:23:00

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.

bobbym · 2010-05-24 01:39:52

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:

soha · 2010-05-31 00:06:42

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

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

bobbym · 2010-05-31 00:08:41

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.

soha · 2010-05-31 00:19:15

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

Math Is Fun Forum

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

Re: Summation

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

Re: Summation

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

Re: Summation

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

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

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