Find the values of x so that the series below converges.?

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.

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