用数学归纳法证明不等式 $1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+K+\frac{1}{\sqrt{n}}<2\sqrt{n}\left(n\in N*\right)$

阅读理解

    The summer vacation is over．Time always flies fast．During the vacation, the weather was hot and I couldn't do much work, but I lived happily．

    Because it was hotter in the afternoon, I did my homework in the morning．I got up at 6：30 am and took a walk in the garden for half an hour．

    After breakfast, I read English and Chinese and did some maths exercises．It took me three hours or more to finish my homework．I worked quite hard and made good progress．

    I spent the afternoon outside．I went to swim and it was fun．I came home at about five or six o'clock．Sometimes a friend of mine would come to see me, and we would spend some time listening to music．

    In this way I spent my vacation happily．I not only studied but also became a good swimmer．Now I'm in good health and in high spirits．