Finding the limit of a sequence (BASIC)

DaveRobinsonUK · 2010-04-24 02:01:31

Hi

After nearly 20yrs since doing any maths, nearly a year ago now I decided to pick up the baton again and via a AS Maths course have eventually come to Sequences and Series. I have been fine so far with Inductive Definition and and I remember Sigma Notation from ages ago. The problem I am having is with Limit of Sequence.

Specifically 'algebraically finding the limit'

I have been battling with this for about 5 days and looking round the internet for something to help but with no avail.

Here is an example

L = 1/2L + 1/4

Hence, 1/2L=1/4 then L = 1/2
Limit is 1/2.

Another example is

(b) Find the limiting value as n tends to infinity.

then it explains

L = 2-1/3L

Hence 4/3L = 2 then L = 3/2
Limit is 1.5.

I am not seeing how 4/3L is coming from L = 2-1/3L and it is causing me problems.

If anyone could help me understand this I would be very grateful.

David

ps. does this site use LaTEX?

bobbym · 2010-04-24 02:06:10

Hi;

After nearly 20yrs since doing any maths, nearly a year ago now I decided to pick up

Forums are a good place to beef up old math muscles. This one is the best.

Yes it does use latex, I have fixed a little bit of your post. Check to see that it is OK.

Just solve for L.

L = 2-1/3L

(4/3)L = 2

L= 2 * (3 / 4) = 3 / 2 = 1.5

That is the fixed point.

DaveRobinsonUK · 2010-04-24 02:27:16

Hi Bobbym

Thank you for getting back so soon, and for the advice about getting back into maths, very rusty, though I am getting better.

It's ,my daughters 2nd Birthday today and we're expecitng a truck load of people a kids around so I'll take a look at it later on.

Thank you

David

bobbym · 2010-04-24 02:33:57

Cool, Happy Birthday to her, and your welcome.

ZHero · 2010-04-24 02:42:52

Hi David!
Welcome to the Forum and Best Wishes on ur daughter's b'day!!

DaveRobinsonUK wrote:

... I am not seeing how 4/3L ...

its easy..

DaveRobinsonUK · 2010-04-25 06:20:36

Hi Guys

Thank you all for you help with this and your support, you are all very kind indeed. And the party went very well. One extremely happy little girl and parents.

O.k, now thats over with, back to the maths.

I found this a couple of times since I restarted, that I have forgotten certain rules regarding Algebra so at times you will just have to bare with me and forgive my ignorance.

So regarding when you add L/3 to the LHS and add it to the L, am I right in considering the L that is added as 3/3L and L/3 as 1/3L.

It seems reasonably straight forward, but I just wanted to be sure before I go on and do my exercises.

Also it would be better for me and others who read my posts if I knew how to write my equations in LaTeX, does anybody know of any good resources from which to learn the basics.

Thanks So Much

David

bobbym · 2010-04-25 06:40:03

Hi David;

Did you save me some cake? Yes, you can say L = ( 3 / 3 ) L so when you add L / 3 you get ( 4 / 3 ) L.

Here is our page on latex.

http://www.mathisfunforum.com/viewtopic.php?id=4397

You can pick it up from there or you can use this page:

http://latex.codecogs.com/editor.php

Which will do it for you.

By the way, Welcome to the forum!

DaveRobinsonUK · 2010-04-26 05:34:01

Yes there is plenty of cake left ;-)

I just did my exercises for finding the limits and got them all correct, so very happy over here
and very grateful too.

This forum is really cool.
D

ZHero · 2010-04-26 06:05:50

DaveRobinsonUK wrote:

.... So regarding when you add L/3 to the LHS and add it to the L, am I right in considering the L that is added as 3/3L and L/3 as 1/3L ...

yes.. you're correct!
just remember that whenever you add two numbers of the form Numerator/Denominator, then just "EQUALIZE the Denominators" and "ADD the Numerators"!

TRY THESE as an exercise if you wish...

also TRY THIS --->
instead of YOUR ---> ;-)

have fun

DaveRobinsonUK · 2010-04-26 08:32:23

Hi ZHero

I have

for the first one, though I am stuck on the second.

The first attempt I expanded the

and multiplied by

from this I got

as my first denominator

I think I am going wrong, becuase things are becoming huge and I think I am going wrong.

Sorry to be a pain.

David

bobbym · 2010-04-26 08:53:59

Hi David;

Hint: Don't expand them.

Just continue with the next fraction.

DaveRobinsonUK · 2010-04-26 09:57:22

Hi Bobby

I think I have it.

Thank you

David

ps
its 11pm here so I'll get off to bed and check this in the morn.

bobbym · 2010-04-26 10:21:25

Hi David;

That is not the right answer. Try plugging in a = 1 and b = 2 to your answer and then plug it into the original problem. Tell me what you get.

ZHero · 2010-04-26 10:44:35

Hi David!

Just think a little over bobbym's hint above!
hint:consider TWO FRACTIONS at time!!

Good Morning

DaveRobinsonUK · 2010-04-27 04:20:23

Hi Bobby and ZHero

when I plug in a = 1 and b=1 to the original problem I get

last time I think I went wrong by factoring out an

I did it again and got this.

however, when I plug a=1 and b=2 into this I definately do not get

Thanks
David

ps. should I continue this on another post about algebraic fractions.

I must seem to you like my daughter seems to me, trying to put the square
into the round hole

bobbym · 2010-04-27 04:25:30

No, you are fine to continue here. When you are simplifying realtionships they may look simpler but they must remain the same. If an expression was 7/ 8 before you simplified it, it should be 7 / 8 afterwards. This is a good numeric test for whether or not you have performed correctly.

Do not worry , I will take you through the rough parts.

Do you follow what has happened above?

DaveRobinsonUK · 2010-04-27 04:32:07

Yes I follow up until this point, I seem to go wrong when adding the next fraction.

bobbym · 2010-04-27 04:41:09

Now let's simplify that a bit. By expanding to try to cancel terms.

DaveRobinsonUK · 2010-04-27 05:03:23

Got it.

Finally

I seemed to be going wrong in the way I was placing my brackets and incorrectly grouping
the terms.

Thank you so much Bobby.

Time for Emma's Dinner and Bath

David

bobbym · 2010-04-27 05:05:08

Hi David;

Since there are no common terms in the numerator and the denominator, we are done.

Math Is Fun Forum

#1 2010-04-24 02:01:31

Finding the limit of a sequence (BASIC)

#2 2010-04-24 02:06:10

Re: Finding the limit of a sequence (BASIC)

#3 2010-04-24 02:27:16

Re: Finding the limit of a sequence (BASIC)

#4 2010-04-24 02:33:57

Re: Finding the limit of a sequence (BASIC)

#5 2010-04-24 02:42:52

Re: Finding the limit of a sequence (BASIC)

#6 2010-04-25 06:20:36

Re: Finding the limit of a sequence (BASIC)

#7 2010-04-25 06:40:03

Re: Finding the limit of a sequence (BASIC)

#8 2010-04-26 05:34:01

Re: Finding the limit of a sequence (BASIC)

#9 2010-04-26 06:05:50

Re: Finding the limit of a sequence (BASIC)

#10 2010-04-26 08:32:23

Re: Finding the limit of a sequence (BASIC)

#11 2010-04-26 08:53:59

Re: Finding the limit of a sequence (BASIC)

#12 2010-04-26 09:57:22

Re: Finding the limit of a sequence (BASIC)

#13 2010-04-26 10:21:25

Re: Finding the limit of a sequence (BASIC)

#14 2010-04-26 10:44:35

Re: Finding the limit of a sequence (BASIC)

#15 2010-04-27 04:20:23

Re: Finding the limit of a sequence (BASIC)

#16 2010-04-27 04:25:30

Re: Finding the limit of a sequence (BASIC)

#17 2010-04-27 04:32:07

Re: Finding the limit of a sequence (BASIC)

#18 2010-04-27 04:41:09

Re: Finding the limit of a sequence (BASIC)

#19 2010-04-27 05:03:23

Re: Finding the limit of a sequence (BASIC)

#20 2010-04-27 05:05:08

Re: Finding the limit of a sequence (BASIC)

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