1² + 3² + 5² + 7² + ........ + 99²

= (1 x 1) + (3 x 3) + (5 x 5) + (7 x 7) + ........... + (99 x 99)

= (1 + 3 + 5 + 7 + ....... + 99) x (1 + 3 + 5 + 7 + ............ + 99)

= {[(99 - 1) : 2 + 1] x (99 + 1) : 2]} +  {[(99 - 1) : 2 + 1] x (99 + 1) : 2]}

= 2500 x 2500

= 6 250 000