By Tolaso in Uncategorized on March 19, 2019 .
This is a very classic exercise and can be dealt with various ways. We know the result in advance. Why? Because it is the Taylor Polynomial of the exponential function. Let us see however how we gonna deal with it with High School Methods.
It follows that . Suppose that . Then the monotony of as well as the sign of is seen at the following table.
For we easily see that the given inequality holds.