因为1/n^3 < 1 / [(n-1)*n*(n+1)] = (1/2)* {1 / [n(n-1)]-1/ [n(n+1)]
所以
a=1^(-3)+2^(-3)+3^(-3)+…+99^(-3)
=1+1/2^3+1/3^3+.+1/99^3
< 1 + (1/2) *{1/(1*2)-1/(2*3)+1/(2*3)-1/(3*4)+ ……+1/(98*99)-1/(99*100)]
=1+(1/2) *{1/(1*2)-1/(99*100)
=1+1/4-1/99*200
< 5/4
即:a< 5/4
则4a< 5
所以4a的整数部分=4