Study the monotony of the string xn = 1/(n-1), n>=2.

To determine if the string, whose general term is xn =
1/(n-1) is increasing or decreasing, we'll have to determine if the difference between 2
consecutive terms of the string is positive or
negative.

We'll have to determine xn+1 =
1/(n+1-1)

xn+1 = 1/n

Now,
we'll calculate the difference:

xn+1 - xn = 1/n  -
1/(n-1)

xn+1 - xn =
(n-1-n)/n(n-1)

xn+1 - xn =
-1/n(n-1)

Since n>=2, the result of the difference
is negative:

-1/n(n-1) < 0 => xn+1 - xn
< 0 => xn+1 < xn

The
string is strictly decreasing: xn+1 < xn.