Power series?

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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!

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