用數(shù)學(xué)歸納法
(1) 當(dāng)n=1時(shí),n^3+3/2n^2+1/2n = 3 是3的倍數(shù)
(2) 設(shè)當(dāng)n=k時(shí),k^3+3/2k^2+1/2k 是3的倍數(shù),則當(dāng)n=k+1時(shí),
(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 + 3k^2 + 6k + 3
= k^3+3/2k^2+1/2k + 3*(k^2+2k+1)
也是3的倍數(shù)
所以,原命題成立.