Question

Tính :

a) A = 1² + 2² + 3² + ... + 20²

b) B = 1 x 2 x 3 + 2 x 3 x 4 + 3 x 4 x 5 + ... + 18 x 19 x 20 

Answer 1

a/ A = 1² + 2² + 3² +...+ 20²

=> A = 1 + 2.( 1 + 1 ) + 3( 1 + 2 ) +...+ 20.( 1 + 19 )

=> A = 1 + 2 + 1.2 + 3 + 2.3 +...+ 20 + 19.20

=> A = ( 1 + 2 + 3 +...+ 20 ) + ( 1.2 + 2.3 +...+ 19.20 )

=>  A = 210 + ( 1.2 + 2.3 +...+ 19.20)

GỌI  ( 1.2 + 2.3 + ... + 19.20 ) là B. Ta có:

B = 1.2 + 2.3 +...+ 19.20

3B = 1.2.3 + 2.3.( 4 - 1 ) +...+ 19.20.( 21 - 18 )

3B = 1.2.3 + 2.3.4 - 1.2.3 + ...+ 19.20.21 - 18.19.20

3B = 19.20.21

B = 19.20.7 

B = 2660

Thay B vào A ta có: 

A= 210 + 2660

A = 2870

Vậy A = 2870

b/ B= 1.2.3 + 2.3.4 + 3.4.5 +...+ 18.19.20

4B = 1.2.3.4 + 2.3.4.( 5-1 ) + 3.4.5.( 6-2 ) +...+ 18.19.20.( 21-17 )

4B= 1.2.3.4 + 2.3.4.5 - 1.2.3.4 + 3.4.5.6 - 2.3.4.5 +...+ 18.19.20.21 - 17.18.19.20

4B = 18.19.20.21

B = \(\frac{18.19.20.21}{4}\) 

B= 18.19.5.21

B = 34200