裂项(怀疑第一项少抄个1)
1+1/2^2+1/3^2+1/4^2+.+1/2002^2 > 1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+.+1/(2002*2003)
右边=1-1/2+1/2-1/3+1/3-1/4.+1/2000-1/2001+1/2001-1/2002
=1-1/2002
=2001/2002
所以 >