n×n!=(n+1)!-n!
1×1!+2×2!+3×3!+4×4!+…2008×2008!+2009×2009!
=(2!-1!)+(3!-2!)+(4!-3!)+……(2009!-2008!)+(2010!-2009!)
=2010!-1!
=2010!-1