Question

1*3+2*5+3*7...1005*2011​

Answer 1

$\it 1\cdot3+2\cdot5+3\cdot7+\ ...\ + 1005\cdot2011=\\ \\ =(1+2\cdot1^2)+(2+2\cdot2^2)+(3+2\cdot3^2)+\ ...\ +(1005+2\cdot1005^2)=\\ \\ =(1+2+3+\ ...\ +1005)+2(1^2+2^2+3^2+\ ...\ +1005^2)$