I had an interesting problem in class today. Find
Now, it's fairly obvious that the answer is 0, the question is how to prove it.
I had an immediate suggestion, obviously if
then the answer is 0. So, we had to prove that.
and M are positive, I can raise them to the degree of n, which is when I get
, which is obviously correct for n>= a certain n0.
Now, my teacher told me this was wrong and the class ended before he could elaborate on why, and the test is next class, which worries me a bit. I do a lot of my proofs this way.
What she said is that we need to prove
, after which we can easily use the squeeze theorem to solve the problem. Unfortunately, I've had no success in proving that statement.
Can you point out where I was wrong in my solution, or help me prove the teacher's statement? I keep getting stuck at
, but the teacher doesn't want us to use e (or infinite geometric series, which would make the proof fairly straightforward by using the binomial formula).
Thank you in advance, I know I'm asking a lot.
Last edited by Bezoux (2014-01-23 06:35:27)