Find the values of ( x ) for which the series converges. (Enter your answer using interval notation.) [ sum_{n=1}^{infty}(x+6)^{n} ] Find the sum of the series for those values of ( x ).
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For a geometric series to converge, the common ratio must be between -1 and 1, i.e., -1 < r < 1. So, we have: -1 < (x+6) < 1 Subtracting 6 from all sides, we get: -7 < x < -5 So, the series converges for x in the interval (-7, -5). Now, for those values of Show more…
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