I'm thinking about the following function, which is a ratio of two finite power series. I'm trying to prove the monotonicity of this function, for arbitrary K.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{\sum_{j=0}^k [(at)^j/j!]}{\sum_{j=0}^k [(bt)^j/j!]}[/tex], and [tex]a>b>0, t>0[/tex]

I know that if k goes to infinity, the function becomes an exponential func. which is increasing in the domain [itex]t \in [0,\infty][/itex]. That is easy. But I'm wondering if this statement is true for arbitrary K.

Any thoughts?

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# Monotonicity of the ratio of two power series

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