B=1.2.3+2.3.4+...+ (n-1).n.(n+1)
=> 4B = 1.2.3.4+2.3.4.4+...+ (n-1)n(n+1).4
=> 4B =1.2.3.4+ 2.3.4.(5-1)+...+ (n-1).n.(n+1).(n+2-(n-2))
=> 4B= 1.2.3.4+2.3.4.5-1.2.3.4+...+ (n-1).n.(n+1)-(n-2).(n-1).n
=> 4B = (n-1).n.(n+1)
=> B= \(\frac{\left(n-1\right)n\left(n+1\right)}{4}\)