What is the sum of the series [math]1 \cdot 1! +2 \cdot 2! +3 \cdot 3! + \ldots + n \cdot n! \;?[/math]
How can i find a partial sum formula for: [math]1\cdot 1!+2\cdot 2!+3\cdot 3!\ldots n\cdot n![/math]?