Question

Power series?

Be sure to indicate the interval on which the power series converges.

Thanks!

Answer 1

Recall the sum of a geometric series is given by

`a/(1 - r)`

We can rewrite our sequence as

`g(x) = 2/(1 - 1/3x)`

`g(x) = (2/3)/(1 - 1/3x)`

Now we can match up coefficients to get

`a = 2/3` and `r = 1/3`

Thus the power series is

`g(x) = 2/3(1/3x)^n`

The interval of convergence will be `(-3, 3)` (because whenever we stray out of this interval we can immediately see that the geometric series diverges.

Hopefully this helps!