Question

Tính A=1.2+2.3+3.4+.....+n.(n+1)

Answer 1

A = 1.2 + 2.3 + 3.4 + ... + n( n + 1 )

3A = 1.2.3 + 2.3.3 + 3.4.3 + ... + n( n + 1 ) . 3

3A = 1.2.3  + 2.3. ( 4 - 1 ) + 3.4. ( 5 - 2 ) + ... + n( n + 1 ) [ ( n + 2 ) - ( n - 1 ) ]

3A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + n ( n + 1 ) , ( n + 2 ) - ( n - 1 ) . n . ( n + 1 ) - n 

3A = n ( n + 1 ) ( n + 2 )

A = n ( n + 1 ) ( n + 2 ) : 3 

Answer 2

A = 1.2 + 2.3 +3.4 + ... + n ( n + 1 )

3A = 1.2.3 + 2.3.3 + 3.4.3 + ... +n ( n + 1 ) . 3

3A = 1.2.3 + 2.3. ( 4 - 1 ) +3.4.( 5 - 2 ) + ... + n ( n +1 ) [ ( n + 2 ) - ( n - 1 ) ]

3A = 1.2.3 + 2.3.4 - 1.2.3 +3.4.5 - 2.3.4 + ... + n ( n +1 ) , ( n + 2 ) - ( n - 1 ) . n . ( n + 1 ) - n

3A = n ( n + 1 ) ( n + 2 ) 

A = n ( n + 1 ) ( n + 2 ) : 3