Question

[Nguyễn Minh Ngọc]

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

chứng minh A=(n-1).n.(n+1):3

Answer 1

[Nobi Nobita]

\(A=1.2+2.3+3.4+.......+\left(n-1\right).n\)

\(\Rightarrow3A=1.2.3+2.3.3+3.4.3+......+\left(n-1\right).n.3\)

\(=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+.....+\left(n-1\right).n.\left[\left(n+1\right)-\left(n-2\right)\right]\)

\(=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+......+\left(n-1\right).n\left(n+1\right)-\left(n-1\right).n\left(n-2\right)\)

\(=\left(n-1\right).n.\left(n+1\right)\)

\(\Rightarrow A=\frac{\left(n-1\right).n.\left(n+1\right)}{3}\)( đpcm )

Answer 2

[Đinh Công An Huy]

lol why lol