can some one prove to me why
is a decreasing sequence?
I know it's obvious but in my textbook they prove it by finding the derivative
which should be which is increasing though right?
Your sequence is obtained by sampling this function is decreasing because its derivative is negative. Because the function is decreasing the sequence obtained by sampling it at is also decreasing.
(you cannot differentiate a sequence because the index is a discrete variable and you need a continuous variable to differentiate)
RonL