Consider the following series. Answer the following questions. ∑n=1 to ∞ x^n/5^n

Question

Consider the following series. Answer the following questions.

∑n=1 to ∞ x^n/5^n

a.  Find the values of 

 a. Find the values for which the series converges: I got (-5,5)

b.  Find the sum of the series for those values of x. Write the formula in terms of x

Not sure how to complete part b.

Answer 1

Your interval of convergence is correct.

This is a geometric series with a=x/5 and r = x/5...you should know how to calculate that!