Find all values of x for which the series converges. (Enter your answer using interval notation.) [infinity] 9 x − 7 9 n n = 0 For these values of x, write the sum of the series as a function of x.

The series converges to       for                  

Step-by-step explanation:

Given the series is    

We have to find the values of x for which the series converges.

We know,

converges to  (a) / (1-r) if r < 1

Otherwise the series will diverge.

Here, is a geometric series with |r| = | 9x |

And it converges for |9x| < 1

Hence, the given series gets converge for

And geometric series converges to

Here, a = 1 and r = 9x

Therefore,

Hence, the given series converges to       for  

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