Question

1×1/5+1/5×1/9+1/9×1/13+···+1/2001×1/2005=?

Answer 1

1×1/5+1/5×1/9+1/9×1/13+···+1/2001×1/2005=1/4(1-1/5)+1/4(1/5-1/9)+...+1/4(1/2001-1/2005) =1/4(1-1/5+1/5+1/9+.+1/2001-1/2005) =1/4(1-1/2005) =501/2005