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

NetherCraft 0

n=1 summation infinity x^n/15^n

Give your answer in interval notation.

( , )

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.

Also Check This  Can you really not eat any popcorn if you have braces?

Leave a Reply

Your email address will not be published. Required fields are marked *