Question

1*2+2*3+3*4+4*5+.+39*40

Answer 1

1*2+2*3+3*4+4*5+.+39*40

=2*(1+3)+4*(3+5)+6*(5+7)+…+38*(37+39)+39*40

=2*(2²+4²+6²+…+38²)+39*40

=8*(1²+2²+3²+…+19²)+39*40

=8*19*(19+1)(2*19+1)/6+39*40

=(4*19/6+1)*39*40

=41/3*39*40

=41*13*40

= 21320