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#1 2007-01-30 08:30:44

RickyOswaldIOW
Member
Registered: 2005-11-18
Posts: 212

Sequences and Series

Write the following series in ∑ notation:

This is a very simple progression but the technique I am using does not seem to yield the right answer, which is:

Here is my method;

Work out the common difference, I subtract the first in the series from the second:

So the difference is 1 -> 1r.  Next I go back one term before the start of the series:

Now I add these two terms together for the general term:

As you can see, I've already gone wrong! But I will continue...  Find the values of r for the first and last terms:

and:

Now I write down the ∑ notation:

This method works fine for the other questions, where am I going wrong?

Last edited by rickyoswaldiow (2007-01-30 08:31:10)


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#2 2007-01-30 08:35:45

Zhylliolom
Real Member
Registered: 2005-09-05
Posts: 412

Re: Sequences and Series

Both of the answers give the same sum, they just look different. If you write out your answer term by term you will see that it is correct.

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#3 2007-01-30 08:38:27

RickyOswaldIOW
Member
Registered: 2005-11-18
Posts: 212

Re: Sequences and Series

I see this, is it then that the answer the book suggests is a simplified version of my answer?  If so, what is the common method to simplify?


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#4 2007-01-30 09:48:02

Ricky
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Registered: 2005-12-04
Posts: 3,791

Re: Sequences and Series

It's like one person saying, "The answer is 1 + 1" and another saying, "No, you're wrong.  The correct answer is 2."


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#5 2007-01-30 10:09:15

pi man
Member
Registered: 2006-07-06
Posts: 251

Re: Sequences and Series

I agree.   Your answer differs from the text book because you're using different ranges of r.   The text book uses r = 2 to 10 and you use r = 1 to 9.    The following would also be a valid (and equal) answer:

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#6 2007-01-30 11:28:18

RickyOswaldIOW
Member
Registered: 2005-11-18
Posts: 212

Re: Sequences and Series

So they'd definately accept my answer?  What I don't understand is - why would they teach me this method that I use on all of their questions, then put the answer in a different format?! It's a crazy world we live in :S


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#7 2007-01-30 11:35:02

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Sequences and Series

They've just simplified it a bit. Instead of having the summation term involving a power of r+1, they've just changed the sum boundaries so that it can be in terms of r instead.

Just like saying that 3/7 * 5/6 = 15/42, but then simplifying it to give 5/14 instead.


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#8 2007-01-31 00:47:37

RickyOswaldIOW
Member
Registered: 2005-11-18
Posts: 212

Re: Sequences and Series

I think I should have made a change in this step:
I've equated

as

Which is just


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