Question: How do I find the interval of convergence of a Taylor series?

I have to copy and paset c(n), and my final results are the square root of what they should be.

```

f:=(x-1)/(x+2)
                               -1 + x
                          f := ------
                               x + 2

plot(f,x=-3..3)

sum(k -> 1/k^2, k=1..1000)
                             1000 f

series(f,x=0);
          1   3     3  2   3   3   3   4   3   5    / 6\
        - - + - x - - x  + -- x  - -- x  + -- x  + O\x /
          2   4     8      16      32      64           

s:=convert(f,FormalPowerSeries)
                          /infinity           \
                          | -----             |
                          |  \     /      k  \|
                          |   )    |   3 x   ||
                 s := 1 + |  /     |- -------||
                          | -----  |        k||
                          \ k = 0  \  2 (-2) //

simplify(s,symbolic)
                 /infinity                       \
                 | -----                         |
                 |  \                            |
                 |   )    /       k  (-k - 1)  k\|
             1 + |  /     \-3 (-1)  2         x /|
                 | -----                         |
                 \ k = 0                         /

                             c := c

c:=k->-(3 *x^k)/((2 (-2)^k))
c(k)
                                  k
                               3 x
                             - ----
                                k  
                               2  x

abs( ((c(k+1)*(x^(k+1)))) / ((c(k)*x^k)));
                               2 |    k   |
                     | (k + 1)|  |   2    |
                     |x       |  |--------|
                                 | (k + 1)|
                                 |2       |
                     ----------------------
                                 2         
                             | k|          
                             |x |          

simplify( % );
                                    2
                          | (k + 1)|
                          |x       |
                          -----------
                                  2  
                              | k|   
                            2 |x |   

L:= limit( %, k=infinity );
                               1    2
                          L := - |x|
                               2     

solve( L<1, x);

```