0.0000000000000000001
05AB1E, 23 bytes

Online compiler can't show all terms for high N but it works fine offline.

Lvy2°*&gt;F„0.0N×yJ,¼¾¹Qiq


Explanation

                          # implicit input X
Lv                        # for each y in range [1 .. X]
  y2°*&gt;F                  # for each N in range [0 .. y*100+1)
        „0.               # push the string "0."
           0N×            # push 0 repeated N times
              y           # push current y
               J,         # join and print
                 ¼¾¹Qiq   # quit the program after X terms printed


Try it online!