Posted by Shawna on Friday, March 21, 2014 at 11:33am.
Use you "sense" of numbers to see what happens to the fractions as n gets larger.
(I think your last term should read 15/(3n^2) or else it becomes large as n gets large)
e.g. look at 5/n
suppose n = 100,000, then 5/n = .00005 , which is close to zero
suppose n = 1,000,000,000 , then 5/n = .000000005, even closer to zero
so as n gets really big
4/n and 5/n each ---> 0
and 15/(3n^2) ---> even faster
so you are stuck with
4 - 0 + 0 + 0 = 4