Question: Working with a serie

Hi all,

> eq := 1/(1+x^8);

                                        1   
                                eq := ------
                                           8
                                      1 + x 
> series(eq, x, 40);

                           8    16    24    32    / 40\
                      1 - x  + x   - x   + x   + O\x  /
> eq1 := Sum((-1)^n*x^(8*n), n = 0 .. infinity);

                                infinity            
                                 -----              
                                  \                 
                                   )        n  (8 n)
                         eq1 :=   /     (-1)  x     
                                 -----              
                                 n = 0              
> eq2 := 4*x^3*eq1;

                                 /infinity            \
                                 | -----              |
                                 |  \                 |
                               3 |   )        n  (8 n)|
                     eq2 := 4 x  |  /     (-1)  x     |
                                 | -----              |
                                 \ n = 0              /
> eq3 := 4*(Sum((-1)^n*x^(8*n+3), n = 0 .. infinity));

                              /infinity                \
                              | -----                  |
                              |  \                     |
                              |   )        n  (8 n + 3)|
                     eq3 := 4 |  /     (-1)  x         |
                              | -----                  |
                              \ n = 0                  /

I want to go from eq2 to eq3 without having to write it by hand.

Thanks in advance

Mario