What is the value of this expression when n approaches infinity?

Question

4−(4/n)+(5/n)+(15/3n^2)

A) 20
B) 10
C) 5
D) 4
E) 1

Answer 1

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