$解：(1)原式=\frac {\sqrt{3}-1}{(\sqrt{3}+1)(\sqrt{3}-1)}+\frac {\sqrt{5}-\sqrt{3}}{(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})}+\frac {\sqrt{7}-\sqrt{5}}{(\sqrt{7}+\sqrt{5})(\sqrt{7}-\sqrt{5})}+···+\frac {\sqrt{121}-\sqrt{119}}{(\sqrt{121}-\sqrt{119})(\sqrt{121}-\sqrt{119})}$
$=\frac {\sqrt{3}-1}2+\frac {\sqrt{5}-\sqrt{3}}2+\frac {\sqrt{7}-\sqrt{5}}2+···+\frac {\sqrt{121}-\sqrt{119}}2$
$=\frac 12×(\sqrt{3}-1+\sqrt{5}-\sqrt{3}+\sqrt{7}-\sqrt{5}+···+\sqrt{121}-\sqrt{119})$
$=\frac 12×(\sqrt{121}-1)$
$=5$
$(2)①∵a=\frac 1{\sqrt{2}-1}=\frac {\sqrt{2}+1}{(\sqrt{2}-1)(\sqrt{2}+1)}=\sqrt{2}+1$
$∴a-1=\sqrt{2} ∴(a-1)^2=2$
$∴a^2-2a+1=2，a^2-2a=1$
$∴3a^2-6a+1=3(a^2-2a)+1=3×1+1=4$
