Question

What are all values of x for which the series n 3^n/x^n converges

Answer 1

The interval of the convergence is x < -3 or x > 3 if the series n 3^n/x^n goes infinitely.

What is convergent of a series?

A series is convergent  if the series of its partial sums approaches a limit; that really is, when the values are added one after the other in the order defined by the numbers, the partial sums getting closer and closer to a certain number.

We can find the interval for the convergent by root test.

Like the Ratio Test, the root Test is used to determine absolute convergence (or not) with factorials, the ratio test is useful.

For the given series:

$\sum^{\infty}_{n=0}\dfrac{3^n}{x^n}$

As the series goes infinitely, we can use root test.

By the root test, the convergence interval will be;

The interval of convergence is:

x < -3 or x > 3   we can write this as:

|x| < 3

Thus, the interval of the convergence is x < -3 or x > 3 if the series n 3^n/x^n goes infinitely.

Learn more about the convergent of a series here:

brainly.com/question/15415793

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