n=1 summation infinity x^n/15^n
Give your answer in interval notation.
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1 Answer

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.