1/1×4+1/4×7+1/7×10+...+1/2002×2005
=(1/3)×(1/1-1/4)+(1/3)×(1/4-1/7)+(1/3)×(1/7-1/10)+...+(1/3)×(1/2002-1/2005)
=(1/3)×(1/1-1/4+1/4-1/7+1/7-1/10+...+1/2002-1/2005)
=(1/3)×(1-1/2005)
=(1/3)×(2004/2005)
=668/2005
1/1×4+1/4×7+1/7×10+...+1/2002×2005
=(1/3)×(1/1-1/4)+(1/3)×(1/4-1/7)+(1/3)×(1/7-1/10)+...+(1/3)×(1/2002-1/2005)
=(1/3)×(1/1-1/4+1/4-1/7+1/7-1/10+...+1/2002-1/2005)
=(1/3)×(1-1/2005)
=(1/3)×(2004/2005)
=668/2005