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Topic: sequences ahhhhhh!!!!! help
Replies: 3   Last Post: Sep 14, 2004 5:24 AM

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Yogi

Posts: 323
Registered: 12/6/04
Re: sequences ahhhhhh!!!!! help
Posted: Sep 10, 2004 11:18 AM
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On 10 Sep 04 10:42:44 -0400 (EDT), sam stewart wrote:
>4 8 16 32
>- + - + -- + --
>1 5 25 125
>
>find ths sum to infinite
>
>I have the formula to work out the sum to infinite but i cant work

out
>what the common difference of the terms are.
>
>Sn to infinite = a1/(1-r)
>(for infinite sequences when -1<r<1)
>
>sn= sum of the first n numbers
>a1 is the first number in the sequence
>r= the common ratio of the sequence
>
>i am sure this is the correct formulae? but what is the common
>difference if you can help me i would be very grateful as i am
>struggling although it may be a very simple question??????
>
>sam


This is, as you suspect, a geometric series but the way it is
written may be misleading you!
Notice that it starts at with "4" rather than 1:
4+ 8/5+ 16/25+ ...

If you take a 4 out of each term:
4(1)+ 4(2/5)+ 4(4/25)+ ...

See what happens? This is simply
4(2/5)^0+ 4(2/5)+ 4(2/5)^2+ ..., a geometric series with common ration
(NOT common "difference") 2/5.

In any geometric series you can find the common ratio by dividing a
term by the preceding term:
8/5 divided by 4 = 2/5
16/25 divided by 8/5= 2/5,
34/125 divided by 16/25= 2/5.

So: a1= 4 and r= 2/5 (which IS between -1 and 1).

Can you find the sum now?







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