1×4＋2×5＋3×6＋…＋n（n＋3）=

1×4＋2×5＋3×6＋…＋n（n＋3）=
1×4＋2×5＋3×6＋…＋n（n＋3）=

1×4＋2×5＋3×6＋…＋n（n＋3）=
原式=1²+3×1+2²+3×2+3²+3×3+……+n²+3n
=(1²+2²+3²+……+n²)+3×(1+2+3+……+n)
=n(n+1)(2n+1)/6+3n(n+1)/2
=n(n+1)(2n+10)/6
=n(n+1)(n+5)/3
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