n(n+5)-(n-3)(n+2)
=(n²+5n) - (n²-n-6)
=6n+6
=6(n+1)
所以 [n(n+5)-(n-3)(n+2)] ÷ 6 = 6(n+1)÷6 = n+1
因为n是正整数,所以n+1也是正整数,
所以对于任意正整数n,式子n(n+5)-(n-3)(n+2)的值都能被6整除