Question

(1/2+1/3+...+1/1997)x(1+1/2+...1/1996)-(1+1/2+...+1/1997)x(1

Answer 1

设1/2+1/3+1/4+...+1/1997=a,1/2+1/3+...+1/1996=b,则

原式=a(1+b)-(1+a)b

=a+ab-b-ab

=a-b

=1/2+1/3+1/4+...+1/1997-(1/2+1/3+...+1/1996)

=1/1997