butterflydreamer
  • butterflydreamer
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 ?? :)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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ganeshie8
  • ganeshie8
Start by finding the common ratio
butterflydreamer
  • butterflydreamer
common ratio = 2cosx
ganeshie8
  • ganeshie8
whats the criterion for geometric series to converge ?

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ganeshie8
  • ganeshie8
common ratio must be between -1 and 1, yes ?
butterflydreamer
  • butterflydreamer
yesss
ganeshie8
  • ganeshie8
-1 < 2cosx < 1 solve x
butterflydreamer
  • butterflydreamer
ohh okay so, \[\frac{ \pi }{ 3 } < x < \frac{ 2\pi}{ 3 } and \frac{ 4\pi }{ 3 } < x < \frac{ 5\pi }{ 3 }\]
ganeshie8
  • ganeshie8
looks good http://www.wolframalpha.com/input/?i=solve+%7C2cos%28x%29%7C%3C1%2C+0%3Cx%3C2pi
butterflydreamer
  • butterflydreamer
thank you :) I forgot about the criterion for geometric series LOL.

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