1X2+2X3+3X4+....NX(N+1)规律

这个数列的通项
an = n(n+1)
即 an = n^2 + n
n(n+1)(2n+1)
其中1^2 + 2^2 + 3^2 + ... + n^2 = --------------
6
n(n+1)
1+2+3+...+n = ------------
2

所以

1X2+2X3+3X4+....NX(N+1)
N(N+1)(2N+1) N(N+1)
= ---------------- + ----------
6 2
N(N+1)(2N+4)
= ----------------------
6
N(N+1)(N+2)
= ------------------------
3

GOOD LUCK~~