Question

Tìm D, biết:

D= 1.2.3 + 2.3.4 + 3.4.5 + ... + 49.50.51

Answer 1

`D=1.2.3+2.3.4+3.4.5+....+49.50.51`

`=>4D=1.2.3.4+2.3.4.4+3.4.5.4+.....+49.50.51`

`=>4D=1.2.3.4+2.3.4.(5-1)+3.4.5.(6-2)+.....+49.50.51.(52-48)`

`=>4D=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+.....+49.50.51.52-48.49.50.51`

`=>4D=49.50.51.52=49.50.51.13.4`

`=>D=13.49.50.51`

Answer 2

Giải:

\(D=1.2.3+2.3.4+3.4.5+...+49.50.51\) 

\(4D=1.2.3.4+2.3.4.\left(5-1\right)+3.4.5.\left(6-2\right)+...+49.50.51.\left(52-48\right)\) 

  \(4D=1.2.3.3.4+2.3.4.5-2.3.4.1+3.4.5.6-3.4.5.2+...+49.50.51.52-49.50.51.48\)

\(4D=49.50.51.52\) 

\(4D=6497400\)  

\(D=6497400:4\)

\(D=1624350\)