Question

1如何计算1*1/4+4*1/7+7*1/10+...+2002*1/2005

Answer 1

1*1/4+4*1/7+7*1/10+...+2002*1/2005

=1/3(1-1/4)+1/3(1/4-1/7)+.+1/3(1/2002-1/2005)

=1/3(1-1/4+1/4-1/7+.+1/2002-1/2005)

=1/3(1-1/2005)

=(1/3)*(2004/2005)

=668/2005