Power series?

enter image source here
Be sure to indicate the interval on which the power series converges.

Thanks!

1 Answer
Noah G
May 16, 2018

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!

Related questions
Impact of this question
1195 views around the world
You can reuse this answer
Creative Commons License