(1)1/2*3+1/3*4+1/4*5.1/2006*2005 (2)1/2+1/(1+1)*(2+1)+1/(1+2)*(2+2).1/(1+2009)*(2+2009) (3)1+1/(1+2)+1/(1+2+3)+.1/(1+2+3+4.100)

(1)1/2*3+1/3*4+1/4*5.1/2006*2005 (2)1/2+1/(1+1)*(2+1)+1/(1+2)*(2+2).1/(1+2009)*(2+2009) (3)1+1/(1+2)+1/(1+2+3)+.1/(1+2+3+4.100)

(1) 1 / 2 * 3 + 1 / 3 * 4 + 1 / 4 * 5.1/2006 * 2005 = 1 / 2 - 1 / 3 + 1 / 3-1 / 4 + 1 / 4-1 / 5 +. + / 12005-1 / 2006 = 1 / 2 - 1 / 2006 = 1002 / 2006 simplify yourself. (2) 1 / 2 + 1 / (1 + 1) * (2 + 1) + 1 / (1 + 2) * (2 + 2). 1 / (1 + 2009) * (2 + 2009) = 1 / 2 + 1 / 2-1 / 3 + 1 / 3