I am thinking if the following condition is in general true: $\frac{n}{m} \leq \frac{\sum_{i = 1} ^ {n} a_i}{\sum_{i = 1} ^ {m} b_i}$, when $n \leq m$ and $a_i \geq 0$, $b_i \geq 0$ but i cannot find a proof.
Can you please help me with that?
I am thinking if the following condition is in general true: $\frac{n}{m} \leq \frac{\sum_{i = 1} ^ {n} a_i}{\sum_{i = 1} ^ {m} b_i}$, when $n \leq m$ and $a_i \geq 0$, $b_i \geq 0$ but i cannot find a proof.
Can you please help me with that?
The condition you mentioned is false. In particular, since you let $a_i = 0$ if we want, let $a_i = 0$ for all $i$, and let $b_i = 1$ or any non-zero number. Then the right side is $0$.