Question

1/2-11/3+21/2-31/3+41/2-51/3+```+9961/2-9971/3+998 简便算法

Answer 1

原式=1/2-1-1/3+2+1/2-3-1/3+4+1/2-5-1/3+```+996+1/2-997-1/3+998

=1/2*409-1/3*409+2-1+3-2+4-3+...+998-997

=1/2*409-1/3*409+409

=409*(1/2-1/3+1)

=409*7/6

=2863/6