原式=(1-根号2)/1-2 + (根号2-根号3)/2-3 +……+(根号99-根号100)/99-100
=-(1-根号2)-(根号2-根号3)-……-(根号99-根号100)
=-1+根号2-根号2+根号3-……-根号99+根号100
=-1+根号100
=根号100-1
原式=(1-根号2)/1-2 + (根号2-根号3)/2-3 +……+(根号99-根号100)/99-100
=-(1-根号2)-(根号2-根号3)-……-(根号99-根号100)
=-1+根号2-根号2+根号3-……-根号99+根号100
=-1+根号100
=根号100-1