Question

(1+1/2+1/3+.+1/2010)×(1/2+1/3+.+1/2011)-(1+1/2+1/3+.+1/2011)

Answer 1

令1/2+1/3+.+1/2010=a,1/2+1/3+.+1/2011=b,则

原式=(1+a)b-(1+b)a

=b+ab-a-ab

=b-a

=(1/2+1/3+.+1/2010+1/2011)-(1/2+1/3+.+1/2010)

=1/2011