# The ratio of two strictly increasing functions

Given: $$f_1(a)=\sum_{i=1}^{k^*-1} \left(\begin{array}{c} K \\\ i \\ \end{array} \right) \left(-1-\frac{1}{ar}\right)^i$$ $$f_2(a)=\sum_{i=1}^{k^*-1} \left(\begin{array}{c} K\\\ i \end{array} \right) \left(-1+\frac{1}{a}\right)^i$$ prove or disprove that $$f_3(a)=\frac{f_1(a)}{f_2(a)}$$ is an increasing funtion of $a$, where $-1< r < 0$ and $0.5 < a < 1$

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Why should we? Where does this question come from? And what is $k^*?$ –  Igor Rivin Apr 24 '12 at 23:23
This question is a part of a more general proof in detection theory where I am working on. $k^{*} > 2$ and $K > k^{*}$ both $k^{*}$ and $K$ are integers. –  Seyhmus Güngören Apr 24 '12 at 23:39
obviously for $k^{*} \geq 2$ too. I will be happy if I will get any answer.d Thanks alot for the visitors of my question.. –  Seyhmus Güngören Apr 24 '12 at 23:47
For the record, I don't think your tags are very appropriate. –  Thierry Zell Apr 25 '12 at 1:25