Question

3分之1+15分之1+35分之1+.1997*1999分之1=

Answer 1

原式=1/(1*3)+1/(3*5)+1/(5*7)+...+1/(1997*1999)

=1/2*(1-1/3)+1/2*(1/3-1/5)+...1/2*(1/5-1/7)+...+1/2(1/1997-1/1999)

=1/2(1-1/3+1/3-1/5+1/5-1/7+...+1/1997-1/1999)

=1/2(1-1/1999)

=999/1999