Find the values of *x* for which the series converges, then find the sum of the series for those values of *x*.

`sum_(n=0)^oo(x-1)^n/5^n`

### 1 Answer | Add Yours

This is a geometric series `sum_(n=0)^oo r^n` , where `r=(x-1)/5.` As with any geometric series, this series converges if and only if `|(x-1)/5|<1.` Solving for `x` gives `-4<x<6.`

**The series converges if and only if** `-4<x<6.`

For these values of `x,` the first term is always `1,` and the ratio between terms is `r.` **The sum is thus**

`1/(1-r)=1/(1-(x-1)/5)=5/(6-x).`

**Sources:**

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes