Question

Tính nhanh

1.2.3+2.3.4+3.4.5+4.5.6+...+20.21.22

 

Answer 1

A = 1.2.3 + 2.3.4 + 3.4.5 + ... + 20.21.22

4A = 1.2.3.4 + 2.3.4.4 + 3.4.5.4 + ... + 20.21.22.4

4A = 1.2.3.4 + 2.3.4.(5 - 1) + 3.4.5.(6 - 2) + ... + 20.21.22.(23 - 19)

4A = 1.2.3.4 + 2.3.4.5 - 1.2.3.4 + 3.4.5.6 - 2.3.4.5 + ... + 20.21.22.23 - 19.20.21.22

4A = 20.21.22.23

A = 20.21.22.23 : 4

A = 53130

Answer 2

Đặt A = 1.2.3 + 2.3.4 + 3.4.5 + 4.5.6 +...+ 20.21.22

\(\Rightarrow4A=1.2.3.4+2.3.4.4+3.4.5.4+4.5.6.4+...+20.21.22.4\)

       \(=1.2.3.4+2.3.4.\left(5-1\right)+3.4.5.\left(6-2\right)+4.5.6.\left(7-3\right)+...+20.21.22.\left(23-19\right)\)  

        = 1.2.3.4 + 2.3.4.5  -1.2.3.4 + 3.4.5.6 - 2.3.4.5 + 4.5.6.7 - 3.4.5.6 +...+ 20.21.22.23 - 19.20.21.22

        =    20.21.22.23

        =  212520

_Hok tốt_

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