N N( +1)(N+2)(N+3)=(N2+3N N)( 2+3N+2) (= N2+3N) (2 +2 N2 +3N)( ) ( )(...

Bài 6: Ta có: ^{n n}

(

⁺¹

)(

ⁿ⁺²

)(

ⁿ⁺³

)

⁼

(

ⁿ

²

^{+3n n}

)(

²

⁺³ⁿ⁺²

) (

^{= n}

²

⁺³ⁿ

) (

²

^{+2 n}

²

⁺³ⁿ

)

( ) ^{( )( )( )} ( )

2

2

+ < + + + < + +3 1 2 3 3 1n n n n n n n n

( )( )( )

⇒ + < + + + < + + ⇒ + + + = +

2

1 2 3 3n n n n n n

( ) ^{( )}

⇒ = + + + + + + +

2

2

2

1 2 ... 3 1 2 ...S n nn n n++ + + =Ta có các công thức :

(

¹

)

1 2 ... ;2

( )( )

n n n

2

2

2

1 2 1n + +1 2 ...6

(

^{1 2}

)(

¹

)

³

(

¹

)

n n n n n⇒ = +S + + +6 2