n=1 summation infinity x^n/15^n
Give your answer in interval notation.
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1 Answer
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The previous answer is INCORRECT.
This series is geometric series. If you apply the ratio test, you will find out that | x / 15 | < 1 is a necessary condition for its convergence. i.e. -15 < x < 15. Now, the series will NOT converge for x = +- 15, as is easily checked... (for instance, the "tail" of the series does NOT go to zero, as n ---> infty.). Hence, the solution set for x is (-15, 15).
Why the previous answer is incorrect: for instance when x = -30, the series reduces to:
Series of (-2) ^n = -2 + 4 -8 + 16 - 24 + ... does NOT converge. The last term does not go to zero, but rather escalates in magnitude.
Hope that helps, thanks.