1. anonymous

@jim_thompson5910

2. jim_thompson5910

|dw:1434074208924:dw|

3. jim_thompson5910

|dw:1434074247695:dw|

4. anonymous

ok

5. jim_thompson5910

the infinite geometric series converges if and only if |r| < 1

6. jim_thompson5910

so if |r| < 1 is true, then it converges otherwise, it diverges

7. jim_thompson5910

if it converges, then the infinite sum is S = a/(1-r)

8. anonymous

and a=-4 right?

9. jim_thompson5910

yep and r = -1/2

10. jim_thompson5910

$\Large \sum_{n=1}^{\infty} {\color{red}{a}}\left({\color{blue}{r}}\right)^{n-1}$ $\Large \sum_{n=1}^{\infty} {\color{red}{-4}}\left({\color{blue}{-\frac{1}{2}}}\right)^{n-1}$

11. anonymous

so it would look like this?

12. jim_thompson5910

yeah because 1-r = 1-(-0.5) = 1+0.5

13. anonymous

Thank you! can you help me with my last problem??

14. jim_thompson5910

sure