Question

1.2+2.3+3.4+........+77.78

Answer 1

Đăt tổng trên là A.Ta có:

3A=1.2.3+2.3.3+3.4.3+...+77.78.3

3A=1.2(3-0)+2.3(4-1).3.4(5-2)+...+77.78(79-76)

3A=(1.2.3-0.1.2)+(2.3.4-1.2.3)+(3.4.5-2.3.4)+...+(77.78.79-76.77.78)

3A=77.78.79

A=77.78.79:3

A=158158

Answer 2

Đặt A = 1.2 + 2.3 + 3.4 + .... + 77.78

<=> 3A = 1.2.3 + 2.3.3 + 3.4.3 + .... + 77.78.3

<=> 3A = 1.2.( 3 - 0 ) + 2.3.( 4 - 1 ) + 3.4.( 5 - 2 ) + .... + 77.78.( 79 - 76 )

<=> 3A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + .... + 77.78.79 - 76.77.78

<=> 3A = 77.78.79

<=> A = ( 77.78.79 ) : 3

=> A = 158158