If $n\in N$, $n>1$ and $\alpha \in [0,1]$ prove that
$$(n^\alpha-(n-1)^\alpha)(2^\alpha+n-n^\alpha-(n-1)^\alpha-1)+(n-1)^\alpha \geq 1$$
EDIT: This is wrong, I misread my own translation as , 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 >.<