20051 × 2 + 20052 × 3 + 20053 × 4 + 20054 × 5 +...+ 20052004 × 2005 =...

20051 × 2 + 20052 × 3 + 20053 × 4 + 20054 × 5 +...+ 20052004 × 2005 =...

20051 × 2 + 20052 × 3 + 20053 × 4 + 20054 × 5 +...+ 20052004 × 2005, = 2005 × (11 × 2 + 12 × 3 + 13 × 4 + 14 × 5 +...+ 12004 × 2005) = 2005 × [(1 - 12) + (12 - 13) + (13 - 14) +...+ (12004 - 12005), = 2005 × [1 - 12005], = 2005 - 2005 × 12005, = 2004.