Prove that the string an=n^2-n is strictly monotonic.

To prove that the given string is strictly monotonic,
we'll have to verify if the difference between 2 consecutive terms is strictly positive
or negative.

Since we know the form of the general term, we
can determine the form of the next  term.

a(n+1) = (n+1)^2
- (n+1)

a(n+1) = n^2 + 2n + 1 - n -
1

a(n+1) = n^2 + n

Now, we'll
check if the difference between a(n+1) and an is strictly positive or negative. If so,
then the string is absolutely monotonic.

a(n+1) - an = n^2
+ n - n^2 + n = 2n > 0

Since n is a natural number
and it is bigger than 1 (n indicates the position of any term in the string), then the
result 2n is strictly positive.

Therefore,
the string whose general term is an = n^2 - n, is strictly
monotonic.