You are Here: Home

# C2 Geometric Series

Announcements Posted on
Take our survey to be in with the chance of winning a £50 Amazon voucher or one of 5 x £10 Amazon vouchers 28-05-2016
1. The sum of the geometric series 1+r+r2+... is k times the sum of the series 1-r+r2..., where k>0. Express r in terms of k.

By equating the sums of both series, I've got (1-rn)/(1-r) = k(1-(-r)n)/(1+r), but I'm struggling from here. Help appreciated.
2. I think you should be looking at the sum to infinity.
3. (Original post by BabyMaths)
I think you should be looking at the sum to infinity.
The question doesn't say anything about the value of r - would you think I could assume that -1<r<1?
Thanks
4. If |r| > 1 then the sum of the series is infinity, so presumable it means not.

Also are you sure about the second series: 1-r+r2 the 'minus' ?
5. (Original post by TrueGrit)
If |r| > 1 then the sum of the series is infinity, so presumable it means not.

Also are you sure about the second series: 1-r+r2 the 'minus' ?
Might mean you multiply by
6. (Original post by Imposition)
Might mean you multiply by
I don't know I didn't write the question...
7. (Original post by TrueGrit)
I don't know I didn't write the question...
More like the question most likely means a geometric series with a ratio of -r. If the minus were a plus, there wouldn't be much of a question.
8. (Original post by TrueGrit)
I don't know I didn't write the question...
I meant that the common ratio is
I think the OP's missing a part of the question out, sum to infinity maybe.
9. (Original post by Imposition)
I meant that the common ratio is
I think the OP's missing a part of the question out, sum to infinity maybe.
Just re-checked the question, it's actually written "the sum of the infinite geometric series 1+r+..." but I'm not sure what it means by infinte series.
10. So, it took you 13 hours to get around to reading the question properly.

If |r|<1 then as you add terms the sum approaches some particular value. For example S = 1+1/2+1/4+1/8+1/16......

The sums are

1
1+1/2=3/2
1+1/2+1/4=7/4
1+1/2+1/4+1/8=15/8

and it's clearly approaching 2 and you can get as close to 2 as you like.
11. (Original post by Julii92)
The sum of the geometric series 1+r+r2+... is k times the sum of the series 1-r+r2..., where k>0. Express r in terms of k.

By equating the sums of both series, I've got (1-rn)/(1-r) = k(1-(-r)n)/(1+r), but I'm struggling from here. Help appreciated.
For infinite geometric series
for |r|<1

Solve for r
then from |r|<1 determine which integer can be k (maybe it's only my question)

## Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
2. this can't be left blank
3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
1. Oops, you need to agree to our Ts&Cs to register

Updated: June 24, 2012
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Today on TSR

### Don't be a half-term hermit

How to revise this week and still have a life

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read here first

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams