Question

[clover]

Chứng minh :   A = 1.2 + 2.3 + 3.4 + 4.5 + ... + n.(n+1) =  \(\frac{n.\left(n+1\right).\left(n+2\right)}{3}\)

Answer 1

[Đào Đức Mạnh]

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

3A=1.2.3+2.3.3+....+3n(n+1)

3A=1.2.3-0.1.2+2.3.4-1.2.3+3.4.5-2.3.4+...+n(n+1)(n+2)-(n-1)n(n+1)

3A=n(n+1)(n+2)

A=n(n+1)(n+2)/3 (đpcm)