Question

A student evaluates the expressions
and
at several different values of
. The student claims, "The value of the expression
is always greater than the value of the expression
."

Which value of
can be used to show that the student's claim is false?


2


4


6


8

Answer 1

2

For example, if the two expressions are (n+2)/(n+1) and (n+1)/n, then for n = 2 we get 4/3 and 3/2, and 4/3 < 3/2, so the claim that the first is always greater is false.