Question

Biết: . Tính: 1.1! + 2.2! + 3.3! + 4.4! + 5.5! = ?

Help me 

Answer 1

1.1!+2.2!+3.3!+4.4!+5.5! 
=(2-1).1!+(3-1).2!+(4-1).3!+ 
(5-1).4!+(6-1).5! 
=2!-1!+3!-2!+4!-3!+5!-4!+6!-5! 
=6!-1!=720-1=719

Answer 2

\(1.1!+2.2!+3.3!+4.4!+5.5!\)

\(=\left(2-1\right)1!+\left(3-1\right)2!+....+\left(6-1\right)5!\)

\(=2!-1!+3!-2!+4!-3!+5!-4!+6!-5!\)

\(=6!-1\)

\(=720-1\)

\(=719\)

Answer 3

1 . 1! + 2 . 2! + 3 . 3! + 4 . 4! + 5 . 5! 

= 1 . 1 + 2 . 1 . 2 + 3 . 1 . 2 . 3 + 4 . 1 . 2 . 3 . 4 + 5 . 1 . 2 . 3 . 4 . 5

= 1 . (1 + 2 . 2 + 3 . 2 . 3 + 4 . 2 . 3 . 4 + 5 . 2 . 3 . 4 . 5)

= 1 . (1 + 4 + 18 + 96 + 600)

= 1 . 719

= 719

Answer 4

Ta có : \(n.n!=\left(n+1-1\right).n!=\left(n+1\right)!-n!\)

\(\Rightarrow1.1!+2.2!+3.3!+4.4!+5.5!=2!-1!+3!-2!+4!-3!+5!-4!+6!-5!=6!-1=719\)