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?

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- March 8th 2008, 12:06 PMakhayoonSequence and bounds (2)
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? - March 8th 2008, 12:19 PMThomas154321
Surely the derivative is just ? Which is negative for , hence decreasing? Unless I'm misreading the question as I've no clue how logs appeared...

But your derivative is also always negative; either way it's decreasing. - March 8th 2008, 12:23 PMakhayoon
I don't think u could do that...or I'm pretty sure...because the variable is a power not a base

- March 8th 2008, 12:30 PMThomas154321
Oh right that was stupid of me, sorry! I redid it and got the same as you. log(1.2) is positive and is also positive, so you definitely have a negative answer which shows decreasing. I don't see the problem.

- March 8th 2008, 12:33 PMakhayoon
no but gets thrown to the denominator right? and theres already a negative sign in front of it

doesn't that make it increase to 0? - March 8th 2008, 12:38 PMThomas154321
Yes as n tends to infinity the derivative tends to 0, but it is never actually 0, it just gets closer and closer. Any value of n you choose will give a negative answer.

- March 9th 2008, 11:22 AMCaptainBlack
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