由条件得 由此可得 .································ 2分 猜测.································································ 4分 用数学归纳法证明: ①当n=1时,由上可得结论成立. ②假设当n=k时,结论成立,即 , 那么当n=k+1时, . 所以当n=k+1时,结论也成立. 由①②,可知对一切正整数都成立.······························· 7分 (Ⅱ). n≥2时,由(Ⅰ)知.·································· 9分 故
综上,原不等式成立. ············································································ 14分 |