Question

Tính nhanh :

1.1!+2.2!+3.3!+......+13.13!

Answer 1

Ta có :

 \(k\cdot k!=\left(k+1-1\right)\cdot k!=\left(k+1\right)\cdot k!-k!\)

Tính 

   \(1\cdot1!+2\cdot2!+3\cdot3!+...+13\cdot13!\)

\(=2!-1!+3!-2!+4!-3!+...+14!-13!\)

\(=-1!+14!=14!-1!\)