从一般到特殊:
因为1+1/N2+1/(N+1)2=(N2(N+1)2+(N+1)2+N2)/(N+1)2N2.=N4+2N3+3N2+2N+1/( )=N2+N+1+N(N2+N+1)+N2(N2+N+1)/ ( )=(N2+N+1)2/(n+1)2N2.开根即得1+1/(N2+N).
所以原式=1+1/2,+1+1/6,+1+1/12,+.+1+1/2003*2004,=2003,+1-1/2,+1/2-1/3,+1/3-1/4,.