Question

Find the following sum and prove your claim:
(1*2)+(2*3)+..+n(n+1).

Answer 1

1*2+2*3+3*4+...+n(n+1)=
(1²+1)+(2²+2)+(3²+3)+...+(n²+n)=
(1² + 2² + 3² + ... + n²) + (1+2+3+...+n)=

`(n(n+1)(2n+1))/(6) * (n(n+1))/(2)` =

`(n(n+1)(n+2))/(3)`