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If $a_i$ and $b_i$ are non-negative values, then can we say about any inequality between the two terms given below

$\frac{1}{k} \sum_i^k \frac{a_i}{b_i}$ and $ \frac{\sum a_i}{\sum b_i}$

It is also given that $a_i \leq b_i$ $\; \forall i$. If so, is there exist a simple proof to show the relation ?

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There is no relation.

$$\frac12\left(\frac14+\frac25\right)<\frac{1+2}{4+5}$$ but $$\frac12\left(\frac24+\frac15\right)>\frac{2+1}{4+5}.$$


Alternatively:

$$\frac12\left(\frac23+\frac{\lambda}{\lambda}\right)=\frac56$$

while

$$\frac{2+\lambda}{3+\lambda}=1-\frac1{3+\lambda}$$ takes any value in $(\frac46,\frac66)$.

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