证明:对于任意整数n,数n/3+n^2/2+n^3/6是整数.怎么证明啊,急22222

问题描述:

证明:对于任意整数n,数n/3+n^2/2+n^3/6是整数.怎么证明啊,急22222

证明:
n/3+n^2/2+n^3/6
=2n/6+3n^2/6+n^3/6
=(2n+3n^2+n^3)/6
=n(2+3n+n^2)/6
=n(n+1)(n+2)/6
因为三个连续整数的乘积能被6整除,即n(n+1)(n+2)能被6整除,
所以 n/3+n^2/2+n^3/6是整数
得证