Math Is Fun Forum

SimonYu

Member

Registered: 2008-07-15

Posts: 6

Help me please!

Hi, im new to this forum but am in dire need of help

The school i attend is, lets say, well below average and only offers me the A Level Maths Course. to go to the universities i want to i need to have at least an AS in Further Maths, so i am self teaching it.

Lets just say im not a good self teacher, and i hate the way that the further maths books dont have colour in them, as i find them harder to follow

do could someone please explain to me the logic behind chapter two - series (yes, i know thats poor , but its hard teaching yourself) as i dont have a clue how they are deriving the forumla or how to work out the identities ad series

Many thanks in advance

Sy

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Sunje Sy
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John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Help me please!

Arithmetic progression
1+ 2+ 3+ 4+ 5+ 6 and reverse:
6+ 5+ 4+ 3+ 2+ 1
________________________
7+ 7+ 7+ 7+ 7+ 7

Last edited by John E. Franklin (2008-07-17 06:32:41)

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igloo myrtilles fourmis

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Help me please!

Geometric progression:
1 +3+ 9+ 27+ 81 and 3 times  this subtracted with big part 1st:

(3 + 9 + 27 + 81 + 243) - (1 + 3 + 9 + 27 + 81) = 243 - 1 =
= 3 series - 1 series = 2 series
So 242 /2 = total  = 121

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igloo myrtilles fourmis

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Help me please!

John, these aren't the sort of series problems Simon has.

The series in further maths are more to do with the method of differences (and using standard results).

Simon, could you post a specific question you are having trouble with?

Last edited by Daniel123 (2008-07-17 06:45:37)

SimonYu

Member

Registered: 2008-07-15

Posts: 6

Re: Help me please!

Ok, for example the first question is use the identity given to find the sum to n terms of a given series, the identity being

1/ r (r + 1) = 1/r - 1/(r +1)

and the series being

n
SIGMA Sign     =    1/ r(r + 1)
r = 1

Sorry im hopeless at typing up maths equations....but i really dont understand what the hell they are on about!

If any one has FP1 then it is chapter two exercises 2 a and b that i am really stuck on

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Sunje Sy
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Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Help me please!

That is known as a telescoping sum.  All of it's middle terms get canceled out, and all your left with is the first term and the limit at the end of it.

Let's look at the first few terms:

Now if we adjust the parenthesis to the right:

See what happens?

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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..."