$ 解：?(1) \frac {1}{3} ×100×101×102=343400 ?$
$?(2)?∵?1×2=\frac {1}{3} (1×2×3-0×1×2)，??2×3=\frac {1}{3} (2×3×4-1×2×3)，?$
$?3×4=\frac {1}{3} (3×4×5-2×3×4)，?···，?n(n+1)=\frac {1}{3} ([n(n+1)(n+2)-(n-1)n(n+1)]?$
$∴?1×2+2×3+···+n(n+1)?$
$?=\frac {1}{3} [1×2×3-0×1×2+2×3×4-1×2×3+3×4×5-4×3×4+···+n(n+1)(n+2)-(n-1)n(n+1)]?$
$?=\frac {1}{3}\ \mathrm {n}(n+1)(n+2)?$
$? (3)?根據(jù)?(2)?的計(jì)算方法，?1×2×3=\frac {1}{4} (1×2×3×4-0×1×2×3)，?$
$?2×3×4=\frac {1}{4} (2×3×4×5-1×2×3×4)，?···，$
$?n(n+1)(n+2)=\frac {1}{4} [n(n+1)(n+2)(n+3)-(n-1)n(n+1)(n+2)]?$
$∴?1×2×3+2×3×4+···+n(n+1)(n+2)?$
$?=\frac {1}{4} [1×2×3×4-0×1×2×3+2×3×4×5-1×2×3×4+···+n(n+1)(n+2)(n+3)-(n-1)n(n+1)(n+2)]?$
$?=\frac {1}{4}\ \mathrm {n}(n+1)(n+2)(n+3)?$
