Answer to Question #60676 in Real Analysis for esita

Question

4. a) Using the principle of mathematical induction, prove that 7 is a factor of
+ ∀ ∈ N
− +
n
n n
3 2 ,
2 1 1
. (4)
b) Show that the equation 0 2 5 12 3 2
x − x + x − = has a root which is a positive real
number. (4)
c) Prove that the set 





, K
8
3
,
7
3
,
6
3
is a countable set.