Math Is Fun Forum

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Simplify the series

I'm stuck, someone please help...

Write in full and simplfy:

But that's as far as I get.. how do you simplify that?

Thanks.

Last edited by Daniel123 (2007-09-12 05:19:22)

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Simplify the series

Last edited by JaneFairfax (2007-09-12 06:38:30)

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Simplify the series

How and why did you add the brackets?... would you mind explaining your thinking please?

thanks.

Last edited by Daniel123 (2007-09-12 06:52:49)

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Simplify the series

As with any finite addition sequence, all addition is associative:

a + (b + c) = (a + b) + c

Subtraction is just like adding a negative, so the same thing applies to subtraction.  So all Jane did was change the order in which you add the terms in a clever way.  It won't change the result, but it will make the result more obvious.  She reflected on the fact that each pair summed to -1.

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"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..."

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Simplify the series

As with any finite addition sequence, all addition is associative

I did not know that. Thank you Ricky, and Jane .

Ok I understand the odd+even pairs make -1, and I understand where the (2k - 1 - 2k) came from, but how do you arrive at -k for the answer?

bossk171

Member

Registered: 2007-07-16

Posts: 305

Re: Simplify the series

In essence, you're going to add -1 over and over again k times. Thus -1-1-1 = -3 and -1-1-1...-1-1 = -k

I didn't mean to steal that answer from anyone, I just got exited that I knew it.

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There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

krassi_holmz

Real Member

Registered: 2005-12-02

Posts: 1,905

Re: Simplify the series

As with any finite addition sequence, all addition is associative:

Absolutely right! That reminds me of this:
as your sum, but goes to infinity:

doesn't converge:

Why do we get different answers?
Because, as ricky pointed, addition is not nessesarly associative with infinite sequences.

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IPBLE:  Increasing Performance By Lowering Expectations.

bossk171

Member

Registered: 2007-07-16

Posts: 305

Re: Simplify the series

Oh, I love stuff like this. What's this technically called, Analysis? I think I covered a little of it in Calculus, but not as much.

Come to think of it, does anyone have any good book recommendations on infinite series?

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There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Simplify the series

Ohhhh I see. Thanks!

Is anyone familiar with AS level maths? If you are.. could you tell me

1) Would they put a question like the one above in the C1 exam?

2) Would they be mean enough to put something as annoying as this in the exam:

By writing down the first four terms, find the recurrence formula that defines:

and the answer is

?

Last edited by Daniel123 (2007-09-12 09:49:20)

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Simplify the series

and the answer is

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Simplify the series

If I remember, C1 only has sequences and nth terms. Series and recurrence relations will come later.

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Why did the vector cross the road?
It wanted to be normal.