1. Sep 21, 2011

### Roscoe1989

1. can someone tell me what r^(n+1)*(1-r)=? I need it to solve a proof, but my math is so rusty! thanks!

2. r^(n+1)*(1-r)

2. Sep 21, 2011

### flyingpig

What is the question...? Like the real question.

3. Sep 21, 2011

### Roscoe1989

prove by induction on n that
1+r+r^2...+r^=1-r^n+1/1-r
if r doesn't equal 1

4. Sep 21, 2011

### flyingpig

Just to be clear, you have

$$r^n + \frac{1}{1 -r}$$ on your right hand side?

5. Sep 21, 2011

### Roscoe1989

oopps, sorry. it should be

1+r+...+r^n=1-r^(n+1) / 1-r

6. Sep 21, 2011

### flyingpig

7. Sep 21, 2011

### flyingpig

Also, shouldn't |r|<1?

8. Sep 21, 2011

### Roscoe1989

the what case?

9. Sep 21, 2011

### flyingpig

Base Case. You know that step you do in Induction

10. Sep 21, 2011

### Roscoe1989

i don't know?

11. Sep 21, 2011

### flyingpig

What can n be and cannot be?

12. Sep 21, 2011

### flyingpig

edit; mistake

13. Sep 21, 2011

### Roscoe1989

is it n can't be 0? but can be anything else?

14. Sep 21, 2011

### Dick

If you don't know induction, just multiply out (1+r+...+r^n)*(1-r). Many terms cancel.

15. Sep 21, 2011

### Roscoe1989

my textbook is saying 1-r^n+1

16. Sep 21, 2011

### flyingpig

Oh sorry I didn't see the 1 in front earlier

Last edited: Sep 21, 2011
17. Sep 21, 2011

### Dick

18. Sep 21, 2011

### flyingpig

try pluggin in 0

19. Sep 21, 2011

### Roscoe1989

n has to be greater than 0

20. Sep 21, 2011

Why?