Question

1*1-2*2+3*3-4*4+5*5-6*6+……-100*100+101*101=

Answer 1

1×1-2×2+3×3-4×4+5×5-6×6+…-100×100+101×101

=101^2-100^2+……+3^2-2^2+1

=(101-100)×(101+100)+……+(3-2)×(3+2)+1

=101+100+99+98+……+2+1

=(101+1)*101/2

=5151