I'm really bad when it comes to proving inequalities. I have prove this:
these are all positive
$\sum\limits_{k=1}^n a_k \leq \sum\limits_{k=1}^n ka_k \leq n \sum\limits_{k=1}^n a_k$
Where would i start with this? Anyone have a simple example i they can show me step by step. I just don't understand how to prove inequalities.
thanks!
Edit
So, would this work: $\sum_{k=1}^\left(n+1\right) a_k = \sum_{k=1}^n a_k + a_\left(k+1\right)$
then subtracting you would get
$2a_\left(k+1\right)$
Now for the right side, do the same thing to get
$2ka_\left(k+1\right)$
Which i now have
$2a_\left(k+1\right) \leq 2ka_\left(k+1\right)$
which reduces to
$1 \leq k$
That finishes the proof for that portion. Am i on the right track for this?