11.2.41-eg-1 - x for which | (-3)( x + 1) | < 1....

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Example Consider the geometric series: X n =0 ( - 3) n ( x + 1) n . Determine the interval of convergence and find the sum of the series on this interval. The geometric series X n =0 r n converges to 1 1 - r provided | r | < 1. Therefore X n =0 ( - 3) n ( x + 1) n is a geometric series with r = ( - 3)( x +1) and the series converges for all values of
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Unformatted text preview: x for which | (-3)( x + 1) | &lt; 1. But | 3 x + 3 | &lt; 1 -1 &lt; 3 x + 3 &lt; 1 -4 &lt; 3 x &lt;-1 -4 3 &lt; x &lt;-1 3 , therefore the interval of convegence is -4 3 ,-1 3 and the series converges to 1 1-(-3 x-3) = 1 4 + 3 x on this interval....
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