1 2 2 , 2 3 2 , 3 4 2 , 4 5 2
Which of the above is the largest?
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
Problem Loading...
Note Loading...
Set Loading...
The general expression for the four terms is a n = n ( n + 1 ) 2 , where n = 1 , 2 , 3 , 4 . Consider the quotient a n a n + 1 , we have:
a n a n + 1 = n + 1 ( n + 2 ) 2 × ( n + 1 ) 2 n = n 3 + 3 n 2 + 3 n + 1 n 3 + 4 n 2 + 4 n > 1 for n ≥ 1
Therefore, a n increases with n , so the largest of the four terms is a 4 = 4 5 2 .