原式=1/2 + (1+2)/3 + (1+2+3)/4 + (1+2+3+4)/5 + ...... + (1+2+3+...+98)/99 + (1+2+3+...+99)/100 - 99/100
= 1/2 + (1+2)2/(2*2) + (1+3)3/(2*4) + (1+4)4/(2*5) + ... + (1+98)98/(2*99) + (1+99)99/(2*100) - 99/100
= (1/2 + 2/2 + 3/2 + ... + 98/2 + 99/2) - 99/100
= (1/2)(1+2+3+...+99) - 99/100
= (1/2)(1+99)99/2 - 99/100
= 25*99 - 99/100
=2474.01
解，原式=1/2+1/3(1+2)+1/4(1+2+3)+，，，
1/99(1+2+3+，，，+99+1/100(1+2+，，+99)-99/100
=1/2+(3/2-1/2)++，，+(100/2-1/2)-99/100
=1/2(1+2+3+，，，+100)-100x1/2-99/100
=2474.01
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