a) Show that n(2n + 1)(7n + 1) is divisible by 6 for all integers n.

b) Find all integers n such that n(2n + 1)(7n + 1) is divisible by 12.

Guest Sep 1, 2020

#2**+2 **

Please put only one question per post.

a) I would prove this using induction. I will outline the method here.

Step 1:

Show true for n=0

Step 2:

Assume true for n=k where k is some integer.

then prove that it will be true for n=k+1 (I've done this myself so I know it works)

Step 3

Assume true for n=k

Prove it is true for n=k-1

Step 4. (Summary)

Since it is true for n=0 it must be true for n=1, n=2 .......etc

also, since it is true for n=0 it must be true for n=-1, n=-2 ..... etc

Therefore it must be true for all integer values of n.

Now try filling in the blanks.

Melody Sep 1, 2020