Question

1x2+2x3+3x4+.........99x100

1x2+2x3+3x4+.........99x100

Answer 1

1x1+2x2+3x3+4x4+......+100x100-(1+2+3+4+.....100)
=100x(100+1)x(2x100+1)/6-(1+100)x100/2
=100x101x201/6-101x100/2
=338350-5050
=333300

Answer 2

=1*(1+1)+2*(2+1)+…+99*(99+1)
=1²+…+99²+1+…+99
=99*(99+1)(2*99+1)/6+99*(99+1)/2
=33*50*199+33*50*3
=33*50*202
=333300