The first elementary paper i'm publising here
Hope to hear some comments
The paper is essentially correct, but there are some careless misprints. For a start, in the result at the start of the paper, the indices k and n are confused. The result $\displaystyle \displaystyle\int_0^{k\pi}\!\!\!\cos^{2n}\theta\,d \theta = \frac{(2k-1)!!}{(2k)!!}(k\pi)$ should read $\displaystyle \displaystyle\int_0^{k\pi}\!\!\!\cos^{2n}\theta\,d \theta = \frac{(2n-1)!!}{(2n)!!}(k\pi)$.
Next, in the statement of Lemma 1, $\displaystyle A_k$ has not yet been defined. You should always define your notation before starting to use it.
Finally, in the section Proving the theorem by Mathematical Induction (First case of Finite Induction), the integral should be equal to $\displaystyle \frac12\pi$, not $\displaystyle \frac12.$
Hi Opalg!
Thank you for your time!
I will correct those mistake that i've made. I will also try to define those terms that i've used. Probably include a short abstract and talk also about second finite induction.
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Hi Dan
Thank you for your time!
I will include the part on integration by parts but essentially it will be very much alike to my Lemma 2. Will try to add more explanatory notes
Probably will add on the case for sine too or leave it for pratice for reader...
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Editted Paper:
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