题目

Do you believe that people’s habits of eating can show their characters and their ways of behavior? Take a look at the following description and find out if it is true for you!The Slow EaterAfter everyone else has finished their meal, you will find this person plodding along, eating one little bite at a time. When sitting down at the table, the slow eater takes his or her sweet time—and is always the last person to finish the meal. Slow eaters are usually people who like to be in control and know how to enjoy their life. They are also usually confident and even-keeled（稳重的）. There若不等式1n+1+1n+2+…+13n+1＞a24对一切正整数n都成立，（1）猜想正整数a的最大值，（2）并用数学归纳法证明你的猜想．