## butterflydreamer one year ago Find those values of x satisfying 0 <= x <= 2pi for which the geometrical series: 1 + 2cosx + 4cos^2x + 8cos^3x + ... has a limiting sum. I'm wondering how we'd approach this question? Maybe by sketching y= cos x for 0 <= x <= 2pi ?? :)

1. ganeshie8

Start by finding the common ratio

2. butterflydreamer

common ratio = 2cosx

3. ganeshie8

whats the criterion for geometric series to converge ?

4. ganeshie8

common ratio must be between -1 and 1, yes ?

5. butterflydreamer

yesss

6. ganeshie8

-1 < 2cosx < 1 solve x

7. butterflydreamer

ohh okay so, $\frac{ \pi }{ 3 } < x < \frac{ 2\pi}{ 3 } and \frac{ 4\pi }{ 3 } < x < \frac{ 5\pi }{ 3 }$

8. ganeshie8
9. butterflydreamer

thank you :) I forgot about the criterion for geometric series LOL.