Question

1/1*5+1/5*9+1/9*13+1/13*17+……+1/2001*2005=?

Answer 1

1/1*5=(1/4)(1-1/5)

1/5*9=(1/4)(1/5-1/9)

.

1/2001*2005=(1/4)(1/2001-1/2005)

所以原式=(1/4)(1-1/5+1/5-1/9.+1/2001-1/2005)

=(1/4)(1-1/2005)=501/2005