Question

B=1.2.3+2.3.4+3.4.5+...+n(n+1)(n+2)

Answer 1

B=1.2.3+2.3.4+3.4.5+...+n.(n+1).(n+2)

4B=4.(1.2.3+2.3.4+3.4.5+...+n.(n+1).(n+2)

4B=1.2.3.4+2.3.4.4+3.4.5.4+...+n.(n+1).(n+2).4

4B=1.2.3.4+2.3.4.(5-1)+3.4.5.(6-2)+...+n.(n+1)+(n+2).(n+3-4)

4B=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+...+n.(n+1).(n+2).(n+3)-(n-1).n.(n+1).(n+2)

4B=(1.2.3.4-1.2.3.4)+(2.3.4.5-2.3.4.5)+...+[(n-1).n.(n+1).(n+2)-(n-1).n.(n+1).(n+2)]+n.(n+2).(n+2).(n+3)

4B=0+0+...+0+n.(n+1).(n+2).(n+3)

4B=n.(n+1).(n+2).(n+3)

B=[n.(n+1).(n+2).(n+3)]:4