Question

证明:对任何正整数n,n^3+3/2n^2+1/2n都是3的倍数

Answer 1

用数学归纳法(1) 当n=1时,n^3+3/2n^2+1/2n = 3 是3的倍数(2) 设当n=k时,k^3+3/2k^2+1/2k 是3的倍数,则当n=k+1时,(k+1)^3+3/2(k+1)^2+1/2(k+1) = k^3+3/2k^2+1/2k + 3k^2 + 3k +3/2(2k+1) + 1/2= k^3+3/2k^2+1/2k + 3...