$解：(1)由题意，得f(30)=30^{2}- 29^{2}= 59$
$(2)因为f(1)=1=2×1-1，f(2)=3=2×2-1， f(3)=5=2×3-1，···，$
$所以依此类推，f(n)=2n-1，$
$所以 f(1)+ f(2)+ f(3)+···+f(40)=1+3+5+···+79=\frac{1+79}{2}×40= 1600$
$(3)因为f(n)=2n－1，$
$则原式=\frac {1}{1×3}+\frac {1}{3×5}+\frac {1}{5×7}+… +\frac {1}{4045×4047}$
$=\frac {1}{2}×(1－\frac {1}{3})+\frac {1}{2}×(\frac {1}{3}－\frac {1}{5})+…+\frac {1}{2}×(\frac {1}{4045}－\frac {1}{4047})$
$=\frac {1}{2}×(1－\frac {1}{3}+\frac {1}{3}－\frac {1}{5}+\frac {1}{5}－\frac {1}{7}+… +\frac {1}{4045}－\frac {1}{4047})$
$=\frac {2023}{4047}$
