⑴猜想：1/n(n+1)=1/n-1/(n+1)
⑵①2010/2011
②1/100-1/(n+1)=(n-99)/100(n+1)
⑶原式=1/4(1/1×2+1/2×3+1/3×4+...+1/1005×1006)
=1/4(1-1/1006)
=1/4×1005/1006
=1005/4024
⑴猜想：1/n(n+1)=1/n-1/(n+1)
⑵①2010/2011
②1/100-1/(n+1)=(n-99)/100(n+1)
⑶原式=1/4(1/1×2+1/2×3+1/3×4+...+1/1005×1006)
=1/4(1-1/1006)
=1/4×1005/1006
=1005/4024