Question: Unable to get correct interval for

I'm trying to find the interval of convergence for the sum

sum((x-2)^n/((x-2)^n),n=0..infinity)

```

c:=n-> 1/(n^2-1)
   c := proc (n) options operator, arrow; 1/(n^2-1) end proc

s:=x-> sum(c(n)*((x-2)^n), n=0..infinity)
 s := proc (x) options operator, arrow; sum(c(n)*x^n, n = 0 ..

    infinity) end proc

# figure out how to plot this, without making it crash
abs( (c(n+1)*x^(n+1)) / (c(n)*x^n) );
                      | (n + 1) / 2    \|
                      |x        \n  - 1/|
                      |-----------------|
                      |/       2    \  n|
                      |\(n + 1)  - 1/ x |

simplify( % );
                          |  / 2    \|
                          |x \n  - 1/|
                          |----------|
                          |n (2 + n) |

L:= limit( %, n=infinity );
                            L := |x|

solve( L<1, x );
                  RealRange(Open(-1), Open(1))

simplify( s(3) )
                            infinity

```

How do I get it to find the correct interval, which is [1,3] I get the correct radius, which is 1.