The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » Math Topics » alt.math.undergrad

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]

Posts: 323
Registered: 12/6/04
Re: sequences ahhhhhh!!!!! help
Posted: Sep 10, 2004 11:18 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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

>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??????

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?

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.