The Heros approximating PI

    Gregory - Leibniz Series

     4       4       4       4       4
    ---  -  ---  +  ---  -  ---  +  ---  ...
     1       3       5       7       9

    

    Nilakantha Series

          4       4       4       4
    3 +  ---  -  ---  +  ---  -  ---     ...
        2*3*4   4*5*6   6*7*8   8*9*10