By using induction, verify that each equation below is true for very positive integer n

1+2+3+......+ n(n+1)= (n(n+1)(n+2)) / 3
who know how to solve this question,pls show the clear step for me,i am preparing for my test

Assume this is true for n=p, then

1+2+3+......+ p(p+1)= (p(p+1)(p+2)) / 3


now put p=p+1 into thr RHS and get

RHS= (p+1)(p+2)(p+3)) / 3
= (p+3)(p+1)(p+2)) / 3, now expand using only the (p+3) factor,
= (p(p+1)(p+2)) / 3 + (p+1)(p+2)

also we know that
(p(p+1)(p+2)) / 3 = 1+2+3+......+ p(p+1), therefore
RHS= 1+2+3+......+ p(p+1) + (p+1)(p+2),

adding the last 2 terms we get

p(p+1) + (p+1)(p+2)= (p+1)(p+2)

therefore
RHS= 1+2+3+......+ p(p+1) + (p+1)(p+2)

which proves the equation