Answer:
1/3(n+1)³
Step-by-step explanation:
1x2+2x3+3x4+4x5+...= 1²+1+2²+2+3²+3+...+n²+n+1=
=(1²+2²+3²+...+n²)+(1+2+3+...+n+1)=
=1/6n(n+1)(2n+1)+1/2(n+1)(1+n+1)=
=1/6(n+1)(n(2n+1)+3(n+2))=
=1/6(n+1)(2n²+4n+2)=
=1/6(n+1)*2(n+1)²=
=1/3(n+1)³
