4. For every integer n 2 1, define an = It at ,t...+. (If k is a positive integer, we define k! (pronounced "k factorial" ) to be k! = 1 . 2 . .. (k-1) . k.) Let A be the set consisting of all the an. Prove that A is bounded above by 3. (You may assume - without proof - standard facts about geometric series. Like geometric series with common ratio 1/2, for example.) The fact that A is bounded above means that A has a supremum. This supremum is called e, and is the base of the natural logarithm. It's also not bigger than 3.]