Question

Find the values of x for which the series converges (write the answer in interval form)

Sum of ((-6)^n)(x^n) starting from n=1 to infinity.

Answer 1

For a series of the form:
\[\sum_{n=1}^{\infty} a^n\]
it converges only if -1 < a < 1

Answer 2

\[-1 < -6x < 1\]
\[-\frac{1}{6} <x < \frac{1}{6}\]

Answer 3

\[x \ne 0\]

Answer 4

Thank you, this really makes sense! But how would I answer a question like: Find the sum of the series for those values of x. when this is an interval answer?