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1. C2 Geometric Series
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. Re: C2 Geometric Series
I think you should be looking at the sum to infinity.
3. Re: C2 Geometric Series
(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. Re: C2 Geometric Series
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' ?
Last edited by TrueGrit; 22-06-2012 at 21:00.
5. Re: C2 Geometric Series
(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. Re: C2 Geometric Series
(Original post by Imposition)
Might mean you multiply by
I don't know I didn't write the question...
7. Re: C2 Geometric Series
(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. Re: C2 Geometric Series
(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. Re: C2 Geometric Series
(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. Re: C2 Geometric Series
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.
Last edited by BabyMaths; 23-06-2012 at 08:43.
11. Re: C2 Geometric Series
(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)
Last edited by ztibor; 24-06-2012 at 09:36.