If $n\in N$, $n>1$ and $\alpha \in [0,1]$ prove that
$$(n^\alpha-(n-1)^\alpha)(2^\alpha+n-n^\alpha-(n-1)^\alpha-1)+(n-1)^\alpha \geq 1$$
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If $n\in N$, $n>1$ and $\alpha \in [0,1]$ prove that
$$(n^\alpha-(n-1)^\alpha)(2^\alpha+n-n^\alpha-(n-1)^\alpha-1)+(n-1)^\alpha \geq 1$$
With all these $ I can't discern what the problem isQuote:
Originally Posted by uyanga
TRANSLATION:
If,
and
prove that
EDIT: This is wrong, I misread my own translation asQuote:
Originally Posted by angel.whiteTRANSLATION:
If
, this problem remains unsolved
Case 1.
TRUE
Case 2.
TRUE
Because Every value of alpha leads this to be true regardless of the value of n, this statement is always true.
Edit:
*sigh* stupid double posts >.<Quote:
Originally Posted by Moo
Hm, but nothing tells us thatis an integer ?
If you can prove that the function is increasing or decreasing, ok :p
not the best morning for me, I read it as being an element of a set containing the integers 0 and 1.Quote:
Originally Posted by MooHm, but nothing tells us that
If you can prove that the function is increasing or decreasing, ok :p
Added a note stating it is not solved.
Listen to the unicorn, she does know all :D
Now the problem is... understand what she says ^^
Actually, your resolution can be used wisely...if the derivative (to
I must be overthinking this, because the solution I was working on just now was much more complicated than a post in "Elementary and Middle School Math Help" should warrant :/
Didn't notice the category :/
Perhaps the student went into the wrong one ?
I solved it.Now it is't hard inequality.(Clapping)
Post it, please, I'm really curious now.Quote:
Originally Posted by uyanga