Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.
|
|
Yogi
Posts:
323
Registered:
12/6/04
|
|
Re: sequences ahhhhhh!!!!! help
Posted:
Sep 10, 2004 11:18 AM
|
|
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?
|
|
|
|
